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)(5hati+hatj-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.
`OC=OA+AC`, where AC is unit vector in direction of AB
`therefore OC=OA+(AB)/(|AB|)`
Similarly, `OC'=OA-(AB)/(|AB|)`