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

Answer: w=(28,-87)

Step-by-step explanation: PLATO

Answer 2

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)`