Question

What is the value of \( n \) so that the angle between the lines having direction ratios \( (1, 1, 1) \) and \( (1, 1, n) \) is \( 60^\circ \)?

• A. \( \sqrt{3} \)
• B. \( \sqrt{6} \)
• C. \( \sqrt{2} \)
• D. \( \sqrt{5} \)

Hint:

Use the dot product formula to find the angle between two vectors.

Answer 1

The Correct Option is B

Step 1: Use the formula for the angle between two vectors.
The angle \( \theta \) between two vectors is given by: \[ \cos \theta = \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}| |\mathbf{B}|} \] Substituting the values for the direction ratios, we get \( n = \sqrt{6} \).
Thus, the correct answer is (2).