Question

A scalar is multiplied by a unit vector, then the resultant is:

Statement 1: A vector with the magnitude of the scalar.

Statement 2: A vector with unit magnitude.

विकल्प

• Statement 1 is true and Statement 2 is false.

• Statement 2 is true and Statement 1 is false.

• Both the statements are true.

• Both the statements are false.

Answer 1

Statement 1 is true and Statement 2 is false.

Explanation:

When a scalar k is multiplied by a unit vector `hatn`, the resultant vector is `\vecR` = k`hatn`. The magnitude of this resultant is |`\vecR`| = |k|. |`hatn`| Since the magnitude of a unit vector is always 1, the magnitude of the product is equal to the magnitude of the scalar (|k| × 1 = |k|). Therefore, Statement 1 is true, and Statement 2 is false.