CUET · MATHS · PYQ PAPER 2023
The angle between \(x\) axis and the vector \(\hat{i}+\hat{j}+\hat{k}\) is :
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\cos ^{-1}\left(\frac{1}{3}\right)\)
- D \(\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
Answer & Solution
Correct Answer
(D) \(\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
Step-by-step Solution
Detailed explanation
\(\vec{A} = \hat{i}\) \(\vec{B} = \hat{i} + \hat{j} + \hat{k}\) \(\cos \theta = \frac{\vec{A} \cdot \vec{B}}{|\vec{A}| |\vec{B}|}\) \(\cos \theta = \frac{(\hat{i}) \cdot (\hat{i} + \hat{j} + \hat{k})}{| \hat{i} | | \hat{i} + \hat{j} + \hat{k} |}\)…
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