Q102 / 150 · MHT CET 2026 (18 April Shift 2) · Physics
If a unit vector is represented by $\vec{U} = 0.9\,\hat{i} - 0.2\,\hat{j} + m\hat{k}$, then the value of m is
- A$0.85$
- Correct answerB$\sqrt{0.15}$
- C$1$
- D$\sqrt{0.77}$
Solution
Given $\vec{U} = 0.9\hat{i} - 0.2\hat{j} + m\hat{k}$ is a unit vector.
The magnitude of a unit vector is $1$.
$|\vec{U}| = \sqrt{(0.9)^2 + (-0.2)^2 + m^2} = 1$
Squaring both sides:
$0.81 + 0.04 + m^2 = 1$
$0.85 + m^2 = 1$
$m^2 = 1 - 0.85$
$m^2 = 0.15$
$m = \sqrt{0.15}$
Answer: $\sqrt{0.15}$
The magnitude of a unit vector is $1$.
$|\vec{U}| = \sqrt{(0.9)^2 + (-0.2)^2 + m^2} = 1$
Squaring both sides:
$0.81 + 0.04 + m^2 = 1$
$0.85 + m^2 = 1$
$m^2 = 1 - 0.85$
$m^2 = 0.15$
$m = \sqrt{0.15}$
Answer: $\sqrt{0.15}$
Hence, the correct answer is option: 'B'.