Question

(d) If vectors \( \mathbf{5i - \lambda j + 2k} \) and \( \mathbf{2i + 3j + 4k} \) are perpendicular, find \( \lambda \):

• A. \( 3 \)
• B. \( 4 \)
• C. \( 6 \)
• D. \( 0 \)

Hint:

Two vectors are perpendicular if their dot product is zero.

Answer 1

The Correct Option is B

Step 1: Use dot product condition \( \mathbf{A} \cdot \mathbf{B} = 0 \). \[ (5)(2) + (-\lambda)(3) + (2)(4) = 0 \] Step 2: Solve for \( \lambda \). \[ 10 - 3\lambda + 8 = 0 \] \[ 18 - 3\lambda = 0 \] \[ \lambda = 4 \]