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JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec a = 2\hat i + \hat j - 2\hat k,\vec b = \hat i + \hat j\). If \(\vec c\) is a vector such that \(\vec a.\vec c = \left| {\vec c} \right|,\left| {\vec c - \vec a} \right| = 2\sqrt 2 \) and the angle between \(\vec a \times \vec b\) and \(\vec c\) is \(30^o\), then \(\left| {\left( {\vec a \times \vec b} \right) \times \vec c} \right|\) equals
- A \(\frac{1}{2}\)
- B \(\frac{{3\sqrt 3 }}{2}\)
- C \(3\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\({\vec{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \vec{b}=\hat{i}+\hat{j}}\) \({\Rightarrow|\vec{a}|=3}\) and \(\vec a \times \vec b = \begin{array}{*{20}{c}} {\hat i}&{\hat j}&{\hat k}\\ 2&1&{ - 2}\\ 1&1&0 \end{array} = 2\hat i - 2\hat j + \hat k\)…
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