JEE Mains · Maths · STD 12 - 10. vector algebra
Let \( \vec{a}=-\hat{i}+\hat{j}+2\hat{k} \), \( \vec{b}=\hat{i}-\hat{j}-3\hat{k} \), \( \vec{c}=\vec{a}\times\vec{b} \) and \( \vec{d}=\vec{c}\times\vec{a} \). Then \( (\vec{a}-\vec{b}) \cdot \vec{d} \) is equal to :
- A 4
- B -4
- C -2
- D 2
Answer & Solution
Correct Answer
(C) -2
Step-by-step Solution
Detailed explanation
\( \vec{d}=(\vec{a}\times\vec{b})\times\vec{a} \) \( \vec{d}=(a^{2})\vec{b}-(\vec{a}\cdot\vec{b})\vec{a} \) \( \vec{d}=6\vec{b}+8\vec{a} \) \( (\vec{a}-\vec{b})\cdot\vec{d} = (\vec{a}-\vec{b})\cdot(6\vec{b}+8\vec{a}) \) \( =8a^{2}-6b^{2}-2\vec{a}\cdot\vec{b} \) \( =48-66+16=-2 \)
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