CUET · MATHS · PYQ PAPER 2025
Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+\hat{k}, \vec{c}=3 \hat{i}+\hat{j}\) be three vectors. If \((\vec{a}+\lambda \vec{b})\) is perpendicular to \(\vec{c}\), then the value of \(\lambda\) is
- A 3
- B 5
- C 2
- D \(- 3\)
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
\((\vec{a}+\lambda \vec{b}) \cdot \vec{c} = 0\) \(( (1-\lambda)\hat{i} + (2+2\lambda)\hat{j} + (3+\lambda)\hat{k} ) \cdot (3 \hat{i}+\hat{j}) = 0\) \((1-\lambda)(3) + (2+2\lambda)(1) = 0\) \(3 - 3\lambda + 2 + 2\lambda = 0\) \(5 - \lambda = 0\) \(\lambda = 5\)
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