TS EAMCET · Maths · Vector Algebra
Let \(\mathbf{p}=\hat{\mathbf{i}}+2 \mathbf{j}-\mathbf{k}, \mathbf{q}=2 \mathbf{i}-\mathbf{j}+\mathbf{k}\). If \(\mathbf{a}\) and \(\mathbf{b}\) are two vectors such that \(\mathbf{p}=\mathbf{a}-2 \mathbf{b}\), \(\mathbf{q}=2 \mathbf{a}+\mathbf{b}\), then the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is
- A \(\cos ^{-1}\left(\frac{3}{2 \sqrt{221}}\right)\)
- B \(\frac{\pi}{2}\)
- C \(\cos ^{-1} \frac{7}{\sqrt{143}}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\cos ^{-1}\left(\frac{3}{2 \sqrt{221}}\right)\)
Step-by-step Solution
Detailed explanation
\(\because \mathbf{p}=\mathbf{a}-2 \mathbf{b}\) and \(\mathbf{q}=2 \mathbf{a}+\mathbf{b}\) So,…
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