Vector Algebra
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
The direction cosines of vector $\hat{i} + 2\hat{j} + 3\hat{k}$ are:
(a) $\left(\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}\right)$
(b) $(1, 2, 3)$
(c) $\left(\frac{1}{14}, \frac{2}{14}, \frac{3}{14}\right)$
(d) $\left(\frac{1}{6}, \frac{2}{6}, \frac{3}{6}\right)$
Step-by-Step Solution
|v| = \sqrt{1+4+9} = \sqrt{14}. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\left(\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}\right)$: 1.0 Mark
Correct Answer: $\left(\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}\right)$
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