JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\vec{i}-\alpha \vec{j}+\beta \hat{k}, \vec{b}=3 \hat{i}+\beta \hat{j}-\alpha \hat{k}\) and \(\vec{c}=-\alpha \hat{i}-2 \hat{j}+\hat{k}\), where \(\alpha\) and \(\beta\) are integers. If \(\vec{a} \cdot \vec{b}=-1\) and \(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}=10\), then \((\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \cdot \overrightarrow{\mathrm{c}}\) is equal to \(.....\)
- A \(8\)
- B \(5\)
- C \(9\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(9\)
Step-by-step Solution
Detailed explanation
\(\vec{a}=(1,-\alpha, \beta)\) \(\vec{b}=(3, \beta,-\alpha)\) \(\vec{c}=(-\alpha,-2,1) ; \alpha, \beta \in I\) \(\vec{a} \vec{b}=-1 \Rightarrow 3-\alpha \beta-\alpha \beta=-1\) \(\Rightarrow \alpha \beta=2\) \(\vec{b} \cdot \vec{c}=10\) \(\Rightarrow-3 \alpha-2 \beta-\alpha=10\)…
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