Question

If the angle \( \theta \) between the line \[ \frac{x + 1}{2} = \frac{z - 2}{2} = \frac{y + 4}{\sqrt{n}} \] and the plane \( 2x - y + z + 4 = 0 \) is such that \( \sin \theta = \frac{1}{3} \), then the value of \( n \) is:

• A. \( \frac{5}{3} \)
• B. \( \frac{3}{5} \)
• C. \( \frac{3}{4} \)
• D. \( \frac{-5}{4} \)

Hint:

The angle between a line and a plane can be found using the direction ratios of the line and the normal to the plane.

Answer 1

The Correct Option is A

Using the formula for the angle between a line and a plane, we can find the value of \( n \) by substituting the given values. After solving, we find \( n = \frac{5}{3} \).