CUET · MATHS · PYQ PAPER 2025
If \(|\vec{a}-\vec{r}|=|\vec{a}|=|\vec{r}|=1\), then angle between \(\vec{a}\) and \(\vec{r}\) is
- A \(\frac{\pi}{3}\)
- B \(\frac{3 \pi}{4}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\(|\vec{a}-\vec{r}|^2 = |\vec{a}|^2 + |\vec{r}|^2 - 2|\vec{a}||\vec{r}|\cos\theta\) \(1^2 = 1^2 + 1^2 - 2(1)(1)\cos\theta\) \(1 = 1 + 1 - 2\cos\theta\) \(1 = 2 - 2\cos\theta\) \(2\cos\theta = 1\) \(\cos\theta = \frac{1}{2}\) \(\theta = \frac{\pi}{3}\)
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