JEE Mains · Maths · STD 12 - 10. vector algebra
The least positive integral value of \(\alpha\), for which the angle between the vectors \(\alpha \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \mathrm{k}\) and \(\alpha \hat{\mathrm{i}}+2 \alpha \hat{\mathrm{j}}-2 \mathrm{k}\) is acute, is
- A \(5\)
- B \(6\)
- C \(7\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
\( \cos \theta=\frac{(\alpha \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \cdot(\alpha \hat{\mathrm{i}}+2 \alpha \hat{\mathrm{j}}-2 \hat{\mathrm{k}})}{\sqrt{\alpha^2+4+4} \sqrt{\alpha^2+4 \alpha^2+4}} \)…
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