JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=-5 \hat{i}+\hat{j}-3 \hat{k}, \vec{b}=\hat{i}+2 \hat{j}-4 \hat{k}\) and \(\vec{c}=(((\vec{a} \times \vec{b}) \times \hat{i}) \times \hat{i}) \times \hat{i}\). Then \(\vec{c} \cdot(-\hat{i}+\hat{j}+\hat{k})\) is equal to
- A \(-12\)
- B \(-10\)
- C \(-13\)
- D \(-15\)
Answer & Solution
Correct Answer
(A) \(-12\)
Step-by-step Solution
Detailed explanation
\(\vec{a}=-5 \hat{i}+j-3 \hat{k}\) \(\vec{b}=\hat{i}+2 \hat{j}-4 \hat{k}\) \((\vec{a} \times \vec{b}) \times \hat{i}=(\vec{a} \cdot \hat{i}) \vec{b}-(\vec{b} \cdot \hat{i}) \vec{a}\) \(=-5 \vec{b}-\vec{a}\) \(=(((-5 \vec{b}-\vec{a}) \times \hat{i}) \times \hat{i})\)…
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