For any two numbers a and b, the product of a − b times itself is equal to a^2 − 2ab + b^2. Does this familiar algebraic result hold for dot products of a vector u − v with itself? In other words, is it true that (u − v) • (u − v) = u • u − 2u • v + v • v? Justify your conclusion, trying not to express vectors u and v in component form.
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Answer:
yes; the distributive property applies to dot products
Step-by-step explanation:
The product of (a-b) with itself is ...
(a -b)·(a -b) = a² -2ab +b²
because the commutative and distributive properties apply to multiplication.
(a -b)·(a -b) = a(a -b) -b(a -b) = a² -ab -ba +b² = a² -ab -ab +b² = a² -2ab +b²
__
The same expansion works for the dot product operation, because the commutative and distributive properties hold for that operation, as well.
(u −v)•(u −v) = u•(u -v) -v•(u -v) = u•u -u•v -v•u +v•v
= u•u -u•v -u•v +v•v = u•u -(u+u)•v +v•v = u•u -2u•v +v•v
_____
Additional comment
The proof of any of the properties of the dot product relies on expressing the vectors in component form. The distributive property is no exception.
Related Questions
May I please receive help?
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It is given that set H such that n(H) = x and H has 8 subsets. Determine the value of x.
A. 2
B. 3
C. 4
D. 8
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Please find the surface area of the pyramid... I will mark you brainliest
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Answer:
S.A. = 704 in²
Step-by-step explanation:
Surface area (S.A. ) = 1/2 lp + B where l is the slant height , p is the perimeter of the base, and B is the area of the base .
Given l = 14; The Base figure is a square so the p = 4· side = 4 · 16 = 64 and the area of the Base = s² = 256
S.A = 1/2 · 14 · 64 + 256
S.A. = 448 + 256
S.A. = 704 in²
Chords AB and CD of a circle intersect.
. AB is divided into two line segments measuring 4 cm and 18 cm.
• CD is divided into two line segments, with the length of one segment twice the length of the other.
What is the length of CD?
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Step-by-step explanation:
line CD, WE and BD are half of the length of CD
Divide: (3x³+4x+11)/(x²-3x+2)
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In attachment I have answered this problem.
5q^2+15q+5=-6 what is the quadratic formula
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Step-by-step explanation:
= −15 ± √5 = 10 the quadratic formula is:10
which expression is equivalent to (-3) x + (-3) (-12)
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Answer:
-3x - 15
or
-3(x + 5)
Step-by-step explanation:
-3x - 3 - 12
-3x - 15
-3(x + 5)
sorry if this doesn't help but i hope it does
Answer:
-3(x + 5)
Step-by-step explanation:
A train is moving at 65.0 m/s. After 16.0 seconds, it is moving at 85.0 m/s. What is the acceleration?
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Happy Holidays!
We can use the following equation to calculate uniform acceleration:
[tex]\large\boxed{a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{\Delta t}}}[/tex]
Plug in the given values to solve:
[tex]\frac{85 - 65}{16}}} = \frac{20}{16} = \boxed{1.25 m/s^2}}[/tex]
Answer:
Hope it will help you...
3 3/8 divided by 1 1/4
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Answer:
Step-by-step explanation:
3 3/8 changes to 27/8 because we multiply 3*8=24 and then add 24 to 3 = 27
same thing for 1 1/4
and then while dividing we flip the left hand side meanig 5/4 becomes 4/5 and division changes to multiplication
Math problem: 3 3/8 divided by 1 1/4
Expand the following expressions and write in standard form. Show your work.
a) (3x + 2)(1 - 4x)
b) (x - 5)^2(2x + 7)
Please help!!!!
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3x(1-4x)+2(1-4x)
3x-12x²+2-8x
-5x-12x²+2
If measure of angle 3 = 74° find each measure NEED HELP ASAP
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A knife is 3x the cost of a spoon9 spoons and 12 knives cost £82.80Work out the cost of 1 knife
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the given cube has a mass of 173 grams, what is it’s density
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Answer:
I think the density is 4cm.
Hope that helps you.
Step-by-step explanation:
Helpppp meee pleaseeee
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Answer:
the correct answer is ( ZYXW ) because the given polygon is a rectangle and its properties is that the opposite sides are equal means the lenght and breath of the unknown side for the big rectangle is 6 , 3 and for small rectangle the the unknown sides are 1 , 2 only so now you've got all the side of both polygons so now you take the ratio of each side and then you can easily find the sides
Step-by-step explanation:
Hope it helps
Have Nice Day : )
Solve by elimination show each step will rate you 5 stars
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Answer:Multiply X + Y by -6 so you can cancel 6x by -6x. Then you get 3y+24. Then divide by 3 and get Y=8 Then solve for X. Use one of the equations and solve for X. I would do X+8=16. Then minus 8 and get 8. So X=8
Step-by-step explanation:
With that being said the coordinate pair would be (8,8)
Francesca is painting a picture of the purple flowers in her garden. She mixes paint to make the perfect color for each type of flower. For the daisies, she mixes 2 ounces of white paint and 5 ounces of purple paint. For the tulips, she mixes 3 ounces of white paint and 6 ounces of purple paint. Which flower is a darker shade of purple?
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Find total ounces mixed for each flower:
Daisies = 2+5 = 7 ounces
Tulips = 3 +6 = 9 ounces
Now find the ratio of purple to white for each one:
Daisies = 5/7 = 0.714
Tulips = 6/9 = 0.666
Daisies have more purple so would be the darker ones.
Answer:
Daisies
Step-by-step explanation:
IXL told me it was right
Can someone plz help :(((((
What is the area, in square inches, of the rectangle?
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Answer:
What are the side lengths?
At a theater, adult tickets for a play cost $15 each and child tickets cost $10 each. If 300 tickets were sold and the sale of the tickets generated between $3575 and $3500, inclusive, what is a possible number of child tickets that were sold?
please help
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Answer:
Answer: 375 adult tickets were sold and 125 children tickets were sold.
what is the standard deviation of 77, 45, 72, 56, 98, 60, 70, 89, 50, 80, 95, 70, 34, 77, 65, 70, 70, 82, 86, 86.
What percentage of the scores are within one standard deviation of the mean (±1)? Please include the range of values for this deviation and the exact values from the data set that are included in this range.
What percentage of the scores are within two standard deviations of the mean (±2)? Please include the range of values for this deviation and the exact values from the data set that are included in this range.
Does this data fit the model of a normal distribution? Why or why not?
Answers
Standard deviation of the numbers is 16.154.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The given observations are
77,45,72,56,98,60,70,89,50,80,95,70,34,77,65,70,70,82,86,86
Average or mean of the data is
x=Sum of n values/ Total number of values
x=1432/20=71.6
The Standard deviation of the data is
[tex]\sigma=\sqrt{\frac{\sum(x-mean)^{2}}{n} }[/tex]
=√5218.8/20
=√260.94
=16.154
Hence, standard deviation of the numbers is 16.154.
To learn more on Statistics click:
https://brainly.com/question/29093686
#SPJ5
(3^3 times 6^6)^-3 in fraction form
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Use cymath! It's free to use and can easily help you with math like this.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(3^3 \times6^6)^{-3}}\\\\\mathsf{3^3}\\\mathsf{=3\times3\times3}\\\mathsf{= 9\times3}\\\mathsf{= 27}\\\\\mathsf{(\bold{27}\times6^6)^{-3}}\\\\\mathsf{6^6}\\\mathsf{= 6\times6\times6\times6\times6\times6}\\\mathsf{= 36\times36\times36}\\\mathsf{= 1,296\times36}\\\mathsf{= 46,656}\\\\\mathsf{(27\times \bold{46,656)}^{-3}}\\\\\mathsf{= \dfrac{1}{1,256,712\times1,256,715\times1,259,712}}\\\\\mathsf{=\dfrac{1}{1,999,004,627,104,432,128}}[/tex]
[tex]\large\text{Therefore, your answer is: }\mathsf{ \dfrac{1 }{1,999,004,627,104,432,128}\ }}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The graph of a function is shown on the grid.
Answers
Answer:
B (0, -2)
Step-by-step explanation:
Since the line intercepts at -2 on the y-axis, -2 is the y-intercept.
what is pls help someone with the problem?2x + 3 = 9
Answers
Answer:
3
Step-by-step explanation:
2x+3=9
2x=9-3
2x=6
2 2
x=3
Answer: x = 3
Step-by-step explanation: 2x+ 3= 9
2x +3 -3 = 9 - 3
2x = 6
2x/2 = 6/2
x = 3
Darin bought a new pair of soccer cleats for $59.99. The sales tax is 6.5%. What is the total cost the Darin will pay?
Answers
Explanation
59.99 x 6.5% = 3.899 = 3.9
59.99 + 3.9 = 63.89
Answer: $63.89
Step-by-step explanation:
In order to find the answer, you have to add the amount charged for the soccer cleats plus the amount of the sales tax.
[tex]59.99 + .065(59.99) = $63.889[/tex]
$63.889 rounded is equal to: $63.89What is the approximate area of the home including the balcony.
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Answer:
LxWxH=A
Step-by-step explanation: multiply LxWxH=A
Please don’t answer just for points! Help is really needed~
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i dont understand
what do we need to do?
2 is 65
3 is 148
4 is 32
I am not sure at all.
A small jar of mustard holds 75% as much as a large jar of mustard. If the large jar holds 36 ounces, how much does the small jar hold?
Answers
Answer:
9 oz
Step-by-step explanation:
36 ounces * 0.75 = 9oz.
Therefore, the small jar holds about 27 ounces.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
the sum of two numbers is 68. the larger number is 14 more than the smaller number. what are the numbers?
Answers
Answer:
The numbers are 27 and 41.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
The numbers would be 41 and 27
Step-by-step explanation:
It would be 41 and 27 because the number we know is 64 so if you divide that by 2 you have 34 (34+34=68) and if you then take half of 14 (14 comes from this part of the question "the larger number is 14 more than the smaller number".) (14/2=7) 7 from one side and add it to the other side you get 41+27=68
(we can also fact check this because your smaller number 27 plus 14 equal 41, then and 41 plus 27 equals 68)
Choose the equations that are not linear equations.
X/2 -y*3 = 1
O - x-y= 2.
x2 + y=4
x= 5
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Answer:
#2 and #4
Step-by-step explanation:
Anything with a variable squared is not linear
Why are the two houses of Congress a compromise? How did this address the concerns of both groups?
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Answer:
To balance the interests of both the small and large states, the Framers of the Constitution divided the power of Congress between the two houses. Every state has an equal voice in the Senate, while representation in the House of Representatives is based on the size of each state's population.
Step-by-step explanation:
part 2 of Question please help me
and thank you for your help
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1 tick represents 8 units