JEE Mains · Maths · STD 12 - 10. vector algebra
If the four points, whose position vectors are \(3 \hat{ i }-4 \hat{ j }+2 \hat{ k }, \hat{ i }+2 \hat{ j }-\hat{ k },-2 \hat{ i }-\hat{ j }+3 \hat{ k } \quad\) and \(5 \hat{ i }-2 \alpha \hat{ j }+4 \hat{ k }\) are coplanar, then \(\alpha\) is equal to
- A \(\frac{73}{17}\)
- B \(-\frac{107}{17}\)
- C \(-\frac{73}{17}\)
- D \(\frac{107}{17}\)
Answer & Solution
Correct Answer
(A) \(\frac{73}{17}\)
Step-by-step Solution
Detailed explanation
Let \(A:(3,-4,2)\) \(C :(-2,-1,3)\) B : \((1,2,-1) \quad\) D : \((5,-2 \alpha, 4)\) \(A, B, C, D\) are coplanar points, then \(\begin{array}{l}\Rightarrow\left|\begin{array}{ccc}1-3 & 2+4 & -1-2 \\ -2-3 & -1+4 & 3-2 \\ 5-3 & -2 \alpha+4 & 4-2\end{array}\right|=0\end{array}\)…
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