Question

If the direction ratios of two mutually perpendicular lines are 5, 2, 4 and 4, 8, x, then the value of x is:

• A. 9
• B. -9
• C. 8
• D. -8

Hint:

For mutually perpendicular lines, the dot product of their direction ratios is zero. This can be used to find the unknown direction ratio.

Answer 1

The Correct Option is B

For two mutually perpendicular lines, the dot product of their direction ratios must be zero. Let's take the direction ratios of the first line as \( 5, 2, 4 \) and the second line as \( 4, 8, x \). The condition for mutual perpendicularity is: \[ 5 \times 4 + 2 \times 8 + 4 \times x = 0. \] Simplifying: \[ 20 + 16 + 4x = 0 \quad \Rightarrow \quad 36 + 4x = 0 \quad \Rightarrow \quad 4x = -36 \quad \Rightarrow \quad x = -9. \] Thus, the correct answer is option (B).