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