Question

Can you help me with this question I can add the answers after

Answer 1

ANSWER

-2.852i + 2.377 j

EXPLANATION

We have to find the projection of u onto v,

$proj_vu=\left(\frac{\vec{u}\cdot\vec{v}}{|v|^2}\right)\vec{v}$

The vectors are:

• u = <-9, -5>

,

• v = <-6, 5>

Let's find the dot product,

$\vec{u}\cdot\vec{v}=u_xv_x+u_yv_y=(-9)(-6)+(-5)(5)=54-25=29$

Now, find the modulus of v squared,

$|\vec{v}|^2=v_x^2+v_y^2=(-6)^2+(5)^2=36+25=61$

Now, we have to divide 29 by 61 and multiply each of the components of vector v by this constant,

$proj_vu=\frac{29}{61}\lt-6,5>\text{ }\approx\text{ }\lt-2.852,2.377>$

Hence, the projection is the vector <-2.852, 2.377> or, using another notation, -2.852i + 2.377 j.