ANSWER:
Second option
[tex]-\: 7.275i-4.244j[/tex]
STEP-BY-STEP EXPLANATION:
Given:
u = -8i - 3j
v = -12i - 7j
We have that the projection of v onto u can be calculated like this:
[tex]\text{proj}_vu=\mleft(\frac{u\cdot\: v}{||v||^2}\mright)\cdot\: v[/tex]
We substitute and can calculate it as follows:
[tex]\begin{gathered} \text{proj}_vu=\mleft(\frac{\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=\frac{117}{193}\cdot(-12i-7j) \\ \text{proj}_vu=-\: 7.275i-4.244j \end{gathered}[/tex]
