The value of a for which the points A,B,C with position vectors `2hati-hatj+hatk, hati-3hatj-5hatk and ahati-3hatj+hatk` respectively are the vertices are the vetices of a righat angled triangle with `C=pi/2` are (A) `-2 and -1` (B) `-2 and 1` (C) `2 and -1` (D) `2 and 1

Options

A. 2 and 1
B. `-2` and -1
C. `-2` and 1
D. 2 and -1

Answer

A

Explanation

`vec(CA)=(2-a)hati+2hatj , vec(CB)=(1-a)hati-6hatk`
`vec(CA).vec(CB)=0 rArr (2-a)(1-a)=0 rArr a=2, 1`