Question

For which value of \(\lambda\) is the vector \(2\hat{i}+\hat{j}-\lambda\hat{k}\) perpendicular to the vector \(\hat{i}+4\hat{j}+\hat{k}\)?

• A. 4
• B. 5
• C. 6
• D. -6

Hint:

Perpendicular vectors have zero dot product; solve 6−λ=0.

Answer 1

The Correct Option is C

Step 1: Perpendicularity condition:
Two vectors are perpendicular exactly when their dot product is zero.

Step 2: Computing the dot product:
\((2\hat i+\hat j-\lambda\hat k)\cdot(\hat i+4\hat j+\hat k)=2(1)+1(4)+(-\lambda)(1)=6-\lambda\).

Step 3: Solving:
Set \(6-\lambda=0\).

Final Answer:
\[ \boxed{\lambda=6} \]