Question

If vector u=(-4,8) and v=(5,-18) vector , which vector can be added to 2u-4v to give the unit vector in the direction of the y-axis as the resultant vector?u

Answer 1

You have two vectors:

$\vec{u}=(-4,8),\\ \\\vec{v}=(5,-18).$

1. Find vector $2\vec{u}-4\vec{v}:$

$2\vec{u}-4\vec{v}=2(-4,8)-4(5,-18)=(-8,16)-(20,-72)=(-8-20,16-(-72))=(-28,88).$

2. If you add vector $\vec{w}=(29,-88)$ to the vector $2\vec{u}-4\vec{v},$ you'll get the sum

$2\vec{u}-4\vec{v}+\vec{w}=(-28,88)+(29,-88)=(1,0).$

Obtained vector is unit vector in the direction of the y-axis.

Answer:  $\vec{w}=(29,-88)$

Answer 2

Answer: w=(28,-87)

Step-by-step explanation: PLATO