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JEE Mains · Maths · STD 12 - 10. vector algebra
If \(\vec a \,\) and \(\vec b \,\) are non-collinear vectors, then the value of \(\alpha \) for which the vectors \(\vec u = \left( {\alpha - 2} \right)\vec a \, + \vec b \) and \(\,\vec v = \left( {2 + 3\alpha } \right)\vec a \, - 3\vec b \) are collinear is :
- A \(\frac{3}{2}\)
- B \(\frac{2}{3}\)
- C \(-\frac{3}{2}\)
- D \(-\frac{2}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
Since, \(\vec u\) and \(\vec v\) are collinear, therefore \(k\vec u + \vec v = 0\) \(\Rightarrow[k(\alpha-2)+2+3 \alpha] \vec{a}+(k-3) \vec{b}=0\) .....\((i)\) since \(\vec{a}\) and \(\vec{b}\) are non-collinear, then for some constant \(m\) and \(n\)…
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