Question:
(d) If vectors \( \mathbf{5i - \lambda j + 2k} \) and \( \mathbf{2i + 3j + 4k} \) are perpendicular, find \( \lambda \):
(d) If vectors \( \mathbf{5i - \lambda j + 2k} \) and \( \mathbf{2i + 3j + 4k} \) are perpendicular, find \( \lambda \):
Show Hint
Two vectors are perpendicular if their dot product is zero.
Updated On: Sep 13, 2025
- \( 3 \)
- \( 4 \)
- \( 6 \)
- \( 0 \)
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The Correct Option is B
Solution and Explanation
Step 1: Use dot product condition \( \mathbf{A} \cdot \mathbf{B} = 0 \).
\[
(5)(2) + (-\lambda)(3) + (2)(4) = 0
\]
Step 2: Solve for \( \lambda \).
\[
10 - 3\lambda + 8 = 0
\]
\[
18 - 3\lambda = 0
\]
\[
\lambda = 4
\]
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