TS EAMCET · Maths · Vector Algebra
If \(\theta\) is the angle between the vectors \(4 \hat{i}-\hat{j}+2 \hat{k}\) and \(\hat{i}+3 \hat{j}-2 \hat{k}\) then \(\sin 2 \theta=\)
- A \(\sqrt{\frac{3}{95}}\)
- B \(-\sqrt{\frac{3}{95}}\)
- C \(-\frac{\sqrt{285}}{49}\)
- D \(\frac{\sqrt{285}}{49}\)
Answer & Solution
Correct Answer
(C) \(-\frac{\sqrt{285}}{49}\)
Step-by-step Solution
Detailed explanation
\(\cos \theta=\frac{(4 \hat{i}-\hat{j}+2 \hat{k}) \cdot(\hat{i}+3 \hat{j}-2 \hat{k})}{\sqrt{21} \times \sqrt{14}}=\frac{-3}{7 \sqrt{6}}\) \(\sin \theta=\sqrt{1-\left(\frac{-3}{7 \sqrt{6}}\right)^2}=\sqrt{1-\frac{9}{49 \times 6}}=\frac{\sqrt{285}}{7 \sqrt{6}}\)…
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