JEE Mains · Maths · STD 12 - 10. vector algebra
Let \( \vec{a}=\hat{i}-2\hat{j}+3\hat{k},\vec{b}=2\hat{i}+\hat{j}-\hat{k},\vec{c}=\lambda\hat{i}+\hat{j}+\hat{k} \) and \( \vec{v}=\vec{a}\times\vec{b} \). If \( \vec{v} \cdot \vec{c}=11 \) and the length of the projection of \( \vec{b} \) on \( \vec{c} \) is \( p \), then \( 9p^{2} \) is equal to:
- A 9
- B 6
- C 4
- D 12
Answer & Solution
Correct Answer
(D) 12
Step-by-step Solution
Detailed explanation
\(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \quad \vec{b}=2 \hat{i}+\hat{j}-\hat{k}, \vec{c}=\lambda \hat{i}+\hat{j}+\hat{k}, \quad\) and \(\vec{v}=\vec{a} \times \vec{b}\). If \(\vec{v} \cdot \vec{c}=11\) \(\vec{v}=(\vec{a} \times \vec{b})=(-\hat{i}+7 \hat{j}+5 \hat{k})\)…
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