Question

What is the terminal point of the vector \mathbf{a}=\left<5,2\right> based at P=\left(4,1\right)?

Answer 1

The terminal point of the given vector is (9,3).

Explanation:

The given vector is

`\mathbf{a}=\left<5,2\right>`

If initial point is
`P(x_1,y_1)` and terminal point is
`Q(x_2,y_2)`, then vector PQ is defined as

`\overrightarrow{PQ}=<x_2-x_1,y_2-y_1>`

Initial point is P=(4,1). Let (a,b) are the coordinates of terminal point.

`<5,2>=<a-4, b-1>`

On comparing both sides we get

`a-4=5\Rightarrow a=5+4\Rightarrow a=9`

`b-1=2\Rightarrow b=2+1\Rightarrow b=3`

Therefore, the terminal point of the given vector is (9,3).