JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\hat{i}+\hat{j}+2 \hat{k}\) and \(\vec{b}=-\hat{i}+2 \hat{j}+3 \hat{k}\). Then the vector product \((\vec{a}+\vec{b}) \times((\vec{a} \times((\vec{a}-\vec{b}) \times \vec{b})) \times \vec{b})\) is equal to:
- A \(5(30 \hat{i}-5 \hat{j}+7 \hat{k})\)
- B \(5(34 \hat{i}-5 \hat{j}+3 \hat{k})\)
- C \(7(30 \hat{i}-5 \hat{j}+7 \hat{k})\)
- D \(7(34 \hat{i}-5 \hat{j}+3 \hat{k})\)
Answer & Solution
Correct Answer
(D) \(7(34 \hat{i}-5 \hat{j}+3 \hat{k})\)
Step-by-step Solution
Detailed explanation
\(\vec{a}=\hat{i}+\hat{j}+2 \hat{k}\) \(\vec{b}=-\hat{i}+2 \hat{j}+3 \hat{k}\) \(\vec{a}+\vec{b}=3 \hat{j}+5 \hat{k} ; \vec{a} \cdot \vec{b}=-1+2+6=7\) \(((\vec{a} \times((\vec{a}-\vec{b}) \times \vec{b})) \times \vec{b})\)…
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