JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\vec{a} = \hat{i} + \hat{j} + \hat{k}\), \(\vec{b} = \hat{j} - \hat{k}\) and \(\vec{c}\) be three vectors such that \(\vec{a} \times \vec{c} = \vec{b}\) and \(\vec{a} \cdot \vec{c} = 3\), then \(\vec{c} \cdot (\vec{a} - 2\vec{b})\) is equal to _______.
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
Given \(\vec{a} \times \vec{c} = \vec{b}\). Taking the dot product with \(\vec{c}\) on both sides: \((\vec{a} \times \vec{c}) \cdot \vec{c} = \vec{b} \cdot \vec{c}\) Since the scalar triple product with two identical vectors is zero, we get: \(\vec{b} \cdot \vec{c} = 0\) We need…
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