Vector Algebra
NCERT Class 12
CBSE
Grade 12
Question:
Find the projection of the vector $\vec{a} = 2\hat{i} + 3\hat{j} + 2\hat{k}$ on the vector $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$.
Step-by-Step Solution
$\vec{a} \cdot \vec{b} = 2 + 6 + 2 = 10, |\vec{b}| = \sqrt{6}$. [1.0 Mark]
$\text{Projection} = \dfrac{10}{\sqrt{6}} = \dfrac{5\sqrt{6}}{3}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating dot product and magnitude: 1.0 Mark
Evaluating scalar projection $= 5\sqrt{6}/3$: 1.0 Mark
Correct Answer:
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