Vector Algebra Question - CBSE

Question

If $\vec{a} = 2\hat{i} + 2\hat{j} + 3\hat{k}, \vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$ and $\vec{c} = 3\hat{i} + \hat{j}$ are such that $\vec{a} + \lambda \vec{b}$ is perpendicular to $\vec{c}$, find $\lambda$.

Accepted Answer

$(\vec{a}+\lambda\vec{b})\cdot\vec{c} = 3(2-\lambda) + 1(2+2\lambda) = 0$. [1.0 Mark]
$8 - \lambda = 0 \Rightarrow \lambda = 8$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Setting up perpendicularity equation: 1.0 Mark
Evaluating $\lambda = 8$: 1.0 Mark

Question:

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