JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=-\hat{i}-\hat{j}+\hat{k}, \vec{a} \cdot \vec{b}=1\) and \(\vec{a} \times \vec{b}=\hat{i}-\hat{j}\). Then \(\vec{a}-6 \vec{b}\) is equal to
- A \(3(\hat{i}-\hat{j}-\hat{k})\)
- B \(3(\hat{i}+\hat{j}+\hat{k})\)
- C \(3(\hat{i}-\hat{j}+\hat{k})\)
- D \(3(\hat{i}+\hat{j}-\hat{k})\)
Answer & Solution
Correct Answer
(B) \(3(\hat{i}+\hat{j}+\hat{k})\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{ a } \times \overrightarrow{ b }=(\hat{ i }-\hat{ j })\) Taking cross product with \(\overrightarrow{ a }\) \(\Rightarrow \quad \vec{a} \times(\vec{a} \times \vec{b})=\vec{a} \times(\hat{i}-\hat{j})\)…
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