JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\vec{a}\) and \(\vec{b}\) are perpendicular, then \(\overrightarrow{ a } \times(\overrightarrow{ a } \times(\overrightarrow{ a } \times(\overrightarrow{ a } \times \overrightarrow{ b })))\) is equal to
- A \(\overrightarrow{0}\)
- B \(\frac{1}{2}|\overrightarrow{ a }|^{4} \overrightarrow{ b }\)
- C \(\overrightarrow{ a } \times \overrightarrow{ b }\)
- D \(|\overrightarrow{ a }|^{4} \overrightarrow{ b }\)
Answer & Solution
Correct Answer
(D) \(|\overrightarrow{ a }|^{4} \overrightarrow{ b }\)
Step-by-step Solution
Detailed explanation
\(\vec{a} \cdot \vec{b}=0\) \(\vec{a} \times(\vec{a} \times \vec{b})=(\vec{a} \cdot \vec{b}) \vec{a}-(\vec{a} \cdot \vec{a}) \vec{b}=-|\vec{a}|^{2} \vec{b}\) Now \(\vec{a} \times\left(\vec{a} \times\left(-|\vec{a}|^{2} \vec{b}\right)\right)\)…
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