TS EAMCET · Maths · Vector Algebra
Let \(\bar{a}=\bar{i}+2 \bar{j}+2 \bar{k}\) and \(\bar{b}=2 \bar{i}-\bar{j}+\mathrm{p} \bar{k}\) be two vectors. If \((\bar{a}, \bar{b})=60^{\circ}\), then \(\mathrm{p}=\)
- A \(\frac{\sqrt{7}}{3 \sqrt{2}}\)
- B \(\frac{3 \sqrt{5}}{\sqrt{7}}\)
- C \(\frac{\sqrt{3}}{\sqrt{7}}\)
- D \(\frac{\sqrt{5}}{\sqrt{7}}\)
Answer & Solution
Correct Answer
(B) \(\frac{3 \sqrt{5}}{\sqrt{7}}\)
Step-by-step Solution
Detailed explanation
\(\cos \theta = \frac{\bar{a} \cdot \bar{b}}{|\bar{a}| |\bar{b}|}\) \(\cos 60^{\circ} = \frac{(1)(2)+(2)(-1)+(2)(\mathrm{p})}{\sqrt{1^2+2^2+2^2}\sqrt{2^2+(-1)^2+\mathrm{p}^2}}\) \(\frac{1}{2} = \frac{2\mathrm{p}}{3\sqrt{5+\mathrm{p}^2}}\) \(3\sqrt{5+\mathrm{p}^2} = 4\mathrm{p}\)…
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