Vector Algebra
NCERT Class 12
CBSE
Grade 12
Question:
The direction cosines of the vector $\hat{i} + 2\hat{j} + 3\hat{k}$ are:
(a) $\dfrac{1}{\sqrt{14}}, \dfrac{2}{\sqrt{14}}, \dfrac{3}{\sqrt{14}}$
(b) $\dfrac{1}{14}, \dfrac{2}{14}, \dfrac{3}{14}$
(c) $1, 2, 3$
(d) $\dfrac{1}{\sqrt{6}}, \dfrac{2}{\sqrt{6}}, \dfrac{3}{\sqrt{6}}$
Step-by-Step Solution
Divide components by magnitude $\sqrt{14}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating direction cosines: 1.0 Mark
Correct Answer: $\dfrac{1}{\sqrt{14}}, \dfrac{2}{\sqrt{14}}, \dfrac{3}{\sqrt{14}}$
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