Question

If two vectors \(\overset{⃗}{A} = 4\hat{i}+n\hat{j}+2\hat{k}\) and \(\overset{⃗}{B} = 2\hat{i}+2\hat{j}-\hat{k}\) are mutually perpendicular to each other then value of 'n' is

• A. \(+3\)
• B. \(+1\)
• C. \(-3\)
• D. \(-1\)

Hint:

Perpendicular vectors have zero dot product.

Answer 1

The Correct Option is C

Step 1: Approach
Check each option in the dot product.

Step 2: Test the options
Dot product $=8+2n-2=6+2n$.
- $n=+3$ gives $12$.
- $n=+1$ gives $8$.
- $n=-3$ gives $0$.
- $n=-1$ gives $4$.

Step 3: Conclusion
Only $n=-3$ gives zero, so the vectors are perpendicular only then. Option (C).

Final Answer:
The dot product 6 + 2n must be zero, so n = -3, option (C). \[ \boxed{-3} \]