If `vec(a)` is a position vector of a point (1, -3) and A is another point (-1, 5), then what are the coordinates of the point B such that `vec(AB)=vec(a)`?

Options

A. (2,0)
B. (0,2)
C. (-2,0)
D. (0,-2)

Answer

B

Explanation

Let the coordinates of B be `(x, y)`.
`vec(a)=hat(i)-3hat(j)`
P.V. of A is `(-1, 5) ` so, `vec(OA)= hat(i) + 5 hat(j) , vec(OB)= x hat(i) + y hat(j)`
`:.vec(AB)=vec(OB)-vec(OA)=vec(a)`
`rArr (x+1) hat(i) + ( y-5) hat(j) = hat(i) - 3 hat(j)`
`rArr x+1=1 and y-5 = -3`
`rArr x=0 and y=2`
`:.` Coordinates of B are (0, 2).