JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\alpha \hat{i}+\hat{j}-\hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0\). If the projection of \(\vec{a} \times \vec{b}\) on the vector \(-\hat{i}+2 \hat{j}-2 \hat{k}\) is \(30 ,\) then \(\alpha\) is equal to
- A \(\frac{15}{2}\)
- B \(8\)
- C \(\frac{13}{2}\)
- D \(7\)
Answer & Solution
Correct Answer
(D) \(7\)
Step-by-step Solution
Detailed explanation
\(\vec{a} \times \vec{b}=(1-\alpha) \hat{i}+\left(\alpha^{2}-2\right) \hat{j}+(\alpha-2) \hat{k}\) Projection of \(\vec{a} \times \vec{b}\) on \(-\hat{i}+2 \hat{j}-2 \hat{k}\) \(=\frac{(\vec{a} \times \vec{b}) \cdot(-\hat{i}+2 \hat{j}-2 \hat{k})}{3}=30\)…
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