A line passes through the points whose position vectors are `hati+hatj-2hatk` and `hati-3hatj+hatk`. The position vector of a point on it at unit distance from the first point is

Options

A. `1/5(5hatihatj-7hatk)`
B. `1/5(4hati+9hatj-15hatk)`
C. `(hati-4hatj+3hatk)`
D. `1/5(hati-4hatj+3hatk)`

Answer

A

Explanation

We have `A(hati+hatj-2hatk)` and `B(hati-3hatj+hatk)`
On line AB points C and `C^(')` are at distance 1 unit from A.
`vec(OC) = vec(OA)+vec(AC)`, where `vec(AC)` is unit vector in direction of `vec(AB)`
`therefore vec(OC) = vec(OA) + (vec(AB))/|AB|`
Similarly `vec(OC^(')) = vec(OA)-(vec(AB))/(vec|AB|)`