1. Tardigrade
  2. Question
  3. Physics
  4. 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?

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Q. 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?

Motion in a Plane

Solution:

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.