JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\overrightarrow{ a }=\alpha \hat{ i }+\beta \hat{ j }+3 \hat{ k }\) \(\overrightarrow{ b }=-\beta \hat{ i }-\alpha \hat{j}-\hat{ k }\) and \(\overrightarrow{ c }=\hat{ i }-2 \hat{ j }-\hat{ k }\) such that \(\overrightarrow{ a } \cdot \overrightarrow{ b }=1\) and \(\overrightarrow{ b } \cdot \overrightarrow{ c }=-3,\) then \(\frac{1}{3}((\vec{a} \times \vec{b}) \cdot \vec{c})\) is equal to ............
- A \(1\)
- B \(4\)
- C \(2\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\vec{a} \cdot \vec{b}=1 \Rightarrow-\alpha \beta-\alpha \beta-3=1\) \(\Rightarrow-2 \alpha \beta=4 \Rightarrow \alpha \beta=-2\) \(........(1)\) \(\vec{b} \cdot \vec{c}=-3 \Rightarrow-\beta+2 \alpha+1=-3\) \(\beta-2 \alpha=4\) \(.......(2)\) Solving \((1)\) and \((2)\),…
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