Question

Given u = −8i − 3j and v = −12i − 7j, what is projvu?

Answer 1

Second option

`-\: 7.275i-4.244j`

Explanation:

Given:

u = -8i - 3j

v = -12i - 7j

We have that the projection of v onto u can be calculated like this:

`\text{proj}_vu=\mleft((u\cdot\: v)/(||v||^2)\mright)\cdot\: v`

We substitute and can calculate it as follows:

`\begin{gathered} \text{proj}_vu=\mleft((\mleft(-8i-3j\mright)\cdot\mleft(-12i-7j\mright))/(\mleft\Vert12i-7j\mleft\Vert^2\mright?\mright?)\mright)\cdot\mleft(-12i-7j\mright) \\ \text{proj}_vu=\frac{\mleft((-8)\cdot(-12)+(-3)\cdot(-7)\mright)}{(-12)^2+(-7^{})^2}\cdot(-12i-7j) \\ \text{proj}_vu=(117)/(193)\cdot(-12i-7j) \\ \text{proj}_vu=-\: 7.275i-4.244j \end{gathered}`