Question

If a unit vector is represented as \( \vec{u} = 0.4\hat{i} + 0.7\hat{j} + c\hat{k} \), then the value of \(c\) is

• A. \( \sqrt{0.11} \)
• B. \( \sqrt{0.25} \)
• C. \( \sqrt{0.65} \)
• D. \( \sqrt{0.35} \)

Hint:

Always use magnitude equals one condition for unit vectors.

Answer 1

The Correct Option is D

Step 1: Condition for a unit vector.
For a unit vector, \[ |\vec{u}| = 1. \]
Step 2: Applying magnitude condition.
\[ (0.4)^2 + (0.7)^2 + c^2 = 1. \] \[ 0.16 + 0.49 + c^2 = 1. \] \[ c^2 = 0.35. \]
Step 3: Conclusion.
\[ c = \sqrt{0.35}. \]