Three Dimensional Geometry
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
The angle between line $\vec{r} = (2\hat{i} - \hat{j} + 3\hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})$ and $\vec{r} = (3\hat{i} + \hat{j} - \hat{k}) + \mu(2\hat{i} + \hat{j} + \hat{k})$ is:
(a) $\cos^{-1}\left(\frac{4}{3\sqrt{2}}\right)$
(b) $\pi/2$
(c) $\pi/4$
(d) $0$
Step-by-Step Solution
cos\theta = (2+1+1)/(\sqrt{3}\sqrt{6}) = 4/\sqrt{18} = 4/(3\sqrt{2}). [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\cos^{-1}\left(\frac{4}{3\sqrt{2}}\right)$: 1.0 Mark
Correct Answer: $\cos^{-1}\left(\frac{4}{3\sqrt{2}}\right)$
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