Vector Algebra
NCERT Class 12
CBSE
Grade 12
Question:
If $\vec{a} = \hat{i} + 2\hat{j} - 3\hat{k}$ and $\vec{b} = 3\hat{i} - \hat{j} + 2\hat{k}$, then the angle between $\vec{a} + \vec{b}$ and $\vec{a} - \vec{b}$ is:
(a) $\dfrac{\pi}{2}$
(b) $\dfrac{\pi}{4}$
(c) $\dfrac{\pi}{3}$
(d) $\pi$
Step-by-Step Solution
$|\vec{a}| = |\vec{b}| = \sqrt{14} \Rightarrow (\vec{a}+\vec{b})\cdot(\vec{a}-\vec{b}) = 0 \Rightarrow \theta = \pi/2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating angle $= \pi/2$: 1.0 Mark
Correct Answer: $\dfrac{\pi}{2}$
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