JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\vec{a}=2 \hat{i}+\hat{j}+2 \hat{k},\) then the value of \(|\hat{ i } \times(\overrightarrow{ a } \times \hat{ i })|^{2}+|\hat{j} \times(\overrightarrow{ a } \times \hat{ j })|^{2}+|\hat{ k } \times(\overrightarrow{ a } \times \hat{ k })|^{2}\) is equal to
- A \(15\)
- B \(27\)
- C \(9\)
- D \(18\)
Answer & Solution
Correct Answer
(D) \(18\)
Step-by-step Solution
Detailed explanation
\(\Sigma|\vec{a}-(\vec{a} \cdot i) i|^{2}\) \(\Rightarrow \quad \Sigma\left(|a|^{2}+(\vec{a} \cdot i)^{2}-2(\vec{a} \cdot i)^{2}\right)\) \(\Rightarrow \quad 3|\vec{a}|^{2}-\Sigma(\vec{a} \cdot i)^{2}\) \(\Rightarrow \quad 2|\vec{a}|^{2}\) \(\Rightarrow \quad 18\)
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