CUET · MATHS · PYQ PAPER 2023
If \(\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k} \& \vec{b}=\hat{i}-3 \hat{j}+5 \hat{k}\) the angle between \(\vec{a}+\vec{b}\) and \(\vec{a}-\vec{b}\) is:
- A \(60^{\circ}\)
- B \(90^{\circ}\)
- C \(120^{\circ}\)
- D \(30^{\circ}\)
Answer & Solution
Correct Answer
(B) \(90^{\circ}\)
Step-by-step Solution
Detailed explanation
\( \vec{u} = \vec{a} + \vec{b} = (5+1)\hat{i} + (-1-3)\hat{j} + (-3+5)\hat{k} = 6\hat{i} - 4\hat{j} + 2\hat{k} \) \( \vec{v} = \vec{a} - \vec{b} = (5-1)\hat{i} + (-1-(-3))\hat{j} + (-3-5)\hat{k} = 4\hat{i} + 2\hat{j} - 8\hat{k} \)…
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