JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\alpha \in R\) and the three vectors \(\vec a = \alpha \hat i + \hat j + 3\hat k\,,\,\vec b = 2\hat i + \hat j - \alpha \hat k\,\) and \(\vec c = \alpha \hat i - 2\hat j + 3\hat k\). Then the set \(S = (\alpha : \vec a, \vec b\) and \(\vec c\) are coplanar)
- A Contains exactly two numbers only one of which is positive
- B is empty
- C Contains exactly two positive numbers
- D is singleton
Answer & Solution
Correct Answer
(B) is empty
Step-by-step Solution
Detailed explanation
\([\vec{a} \cdot \vec{b} \cdot \vec{c}]=0\) \(\left| {\begin{array}{*{20}{c}} \alpha &3&1\\ 2&1&{ - \alpha }\\ \alpha &{ - 2}&3 \end{array}} \right| = 0\) \(\alpha(3-2 \alpha)+1\left(-\alpha^{2}-6\right)+3(-4-\alpha)=0\) \(3 \alpha-2 \alpha^{2}-\alpha^{2}-6-12-3 \alpha=0\)…
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