CUET · MATHS · PYQ PAPER 2023
If \(\vec{a}\) and \(\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) for \(\vec{a}+\sqrt{3 b}\) to be a unit vector is given by :
- A \(\frac{\pi}{6}\)
- B \(\frac{5 \pi}{6}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{2 \pi}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{5 \pi}{6}\)
Step-by-step Solution
Detailed explanation
\((|\vec{a} + \sqrt{3}\vec{b}|)^2 = 1^2\) \(|\vec{a}|^2 + 2\sqrt{3}|\vec{a}||\vec{b}|\cos\theta + 3|\vec{b}|^2 = 1\) \(1^2 + 2\sqrt{3}(1)(1)\cos\theta + 3(1^2) = 1\) \(1 + 2\sqrt{3}\cos\theta + 3 = 1\) \(4 + 2\sqrt{3}\cos\theta = 1\) \(2\sqrt{3}\cos\theta = -3\)…
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