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Vectors u and v are shown in the graph. What is projvu?

Vectors u and v are shown in the graph. What is projvu?-example-1
User DoubleYou
by
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1 Answer

6 votes

In order to calculate the projection of u on v, we can use the formula below:


proj_vu=(u\cdot v)/(||v||^2)\cdot v

First, let's define the vectors u and v from the image:


\begin{gathered} u=-10i-7j\\ \\ v=-8i+4j \end{gathered}

Now, let's calculate the dot product on the numerator:


u\cdot v=(-10)(-8)+(-7)(4)=80-28=52

The denominator can be calculated as the dot product of v and itself:


v^2=v\cdot v=(-8)(-8)+(4)(4)=64+16=80

Therefore the projection is given by:


prov_vu=(52)/(80)\cdot(-8i+4j)=-5.2i+2.6j

Correct option: the second one.

User Stephen Blum
by
7.7k points
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