JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\overrightarrow{ a } \cdot \overrightarrow{ b }=1, \overrightarrow{ b } \cdot \overrightarrow{ c }=2\) and \(\overrightarrow{ c } \cdot \overrightarrow{ a }=3\), then the value of \([\vec{a} \times(\vec{b} \times \vec{c}), \vec{b} \times(\vec{c} \times \vec{a}), \vec{c} \times(\vec{b} \times \vec{a})]\) is
- A \(0\)
- B \(-6 \overrightarrow{ a } \cdot(\overrightarrow{ b } \times \overrightarrow{ c })\)
- C \(12 \overrightarrow{ c } \cdot(\overrightarrow{ a } \times \overrightarrow{ b })\)
- D \(-12 \vec{b} \cdot(\vec{c} \times \vec{a})\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ a } \times(\overrightarrow{ b } \times \overrightarrow{ c })=(\overrightarrow{ a } \cdot \overrightarrow{ c }) \overrightarrow{ b }-(\overrightarrow{ a } \cdot \overrightarrow{ b }) \overrightarrow{ c }=3 \overrightarrow{ b }-\overrightarrow{ c }\)…
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