Question

Unit vector
I. has dimensions and a unit.
II. has unit magnitude.
III. when multiplied by a scalar results in a scalar.
Which of the following statement(s) is/are incorrect?

• A. Both I and II
• B. Only II
• C. Both I and III
• D. Both II and III

Answer 1

Answer: (C)

A unit vector is a vector of unit magnitude and points in a particular direction.
It has no unit and dimensions. It is just used to specify a direction only.
If we multiply a unit vector, say $\hat{n}$ by a scalar $\lambda$, then the result is a vector $=\lambda \hat{n}$.
So, statements I and III are incorrect but II is correct.