AP EAMCET · Maths · Vector Algebra
Let \(\bar{a}=2 \bar{i}+\bar{j}-2 \bar{k}\) and \(\bar{b}=\bar{i}+\bar{j}\) be two vectors. If \(\bar{c}\) is a vector such that \(\bar{a} \cdot \bar{c}=|\bar{c}|,|\bar{c}-\bar{a}|=2 \sqrt{2}\) and the angle between \(\bar{a} \times \bar{b}\) and \(\bar{c}\) is \(30^{\circ}\), then \(|(\bar{a} \times \bar{b}) \times \bar{c}|=\)
- A \(\frac{2}{3}\)
- B \(\frac{3}{2}\)
- C 2
- D 3
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(\bar{a} \times \bar{b} = \begin{vmatrix} \bar{i} & \bar{j} & \bar{k} \\ 2 & 1 & -2 \\ 1 & 1 & 0 \end{vmatrix} = (0 - (-2))\bar{i} - (0 - (-2))\bar{j} + (2 - 1)\bar{k} = 2\bar{i} - 2\bar{j} + \bar{k}\) \(|\bar{a}| = \sqrt{2^2+1^2+(-2)^2} = \sqrt{4+1+4} = \sqrt{9} = 3\)…
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