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Vector Algebra
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
If $\vec{a} = 2\hat{i} + 2\hat{j} + 3\hat{k}, \vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$ and $\vec{c} = 3\hat{i} + \hat{j}$ such that $\vec{a} + \lambda \vec{b}$ is perpendicular to $\vec{c}$, find $\lambda$.
Step-by-Step Solution
Given: If $\vec{a} = 2\hat{i} + 2\hat{j} + 3\hat{k}, \vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$ and $\vec{c} = 3\hat{i} + \hat{j}$ such that $\vec{a} + \lambda \vec{b}$ is perpendicular to $\vec{c}$, find $\lambda$. Step 1: Set up the governing mathematical relation / formula: From the given problem statement, we state the key relation: $$(a + \lambda b) . c$$ [1.0 Mark] Step 2: Execute step-by-step evaluation and simplify: Evaluating and simplifying the expression: $$8.$$ [1.0 Mark] Conclusion: The solution is verified as 8..
--- 🎯 Official CBSE Marking Scheme: Setting up equation / formula: 1.0 Mark Evaluating correct final answer: 1.0 Mark
Correct Answer:
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