A scalar is multiplied by a unit vector, then the resultant is: Statement 1: A vector with the…
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.
- aStatement 1 is true and Statement 2 is false.
- bStatement 2 is true and Statement 1 is false.
- cBoth the statements are true.
- dBoth the statements are false.
Answer
Answer
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Correct option: a
Answer: (a) Statement 1 is true and Statement 2 is false.
Multiplying a scalar $k$ by a unit vector $\hat{u}$ produces $\vec{v} = k\hat{u}$ with magnitude $|k\hat{u}| = |k||\hat{u}| = |k|$, which equals the magnitude of the scalar. The magnitude is not unit in general, so Statement 2 is false.
From ISC 2026 Mathematics Paper 1, question 15(i).