Question

What if we multiply a scalar to the unit vector?

(a) The direction will change accordingly

(b) The magnitude will change accordingly

(c) The magnitude will not change accordingly

(d) The direction will change by a factor of square root of the scalar

I got this question in an interview for job.

The origin of the question is Cartesian Vectors topic in division Force Vectors of Engineering Mechanics

Answer 1

Right option is (b) The magnitude will change accordingly

Easiest explanation: The magnitude of the unit vector will change by the amount of the scalar multiplied. Not the direction. Because the direction is being fixed after the application of the unit vector’s calculation. That is the vector divided by its magnitude.