Question

If mi+2mj is a unit vector, then the value of ‘m’ is A. 1/9 B.1/4 C.1/3 D.1/2

Answer 1

Let v = m i + 2 m j. Then |v| = sqrt(m^2 + (2m)^2) = sqrt(5 m^2) = |m| sqrt5. For v to be a unit vector |v| = 1, so |m| = 1/√5 and hence m = ±1/√5 ≈ ±0.4472.

None of the given options (1/9, 1/4, 1/3, 1/2) equals 1/√5, so the correct value is m = ±1/√5 (positive value 1/√5 if only positive m is allowed).