Question

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

Answer 1

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.