AP EAMCET · Maths · Three Dimensional Geometry
If the four points \((6,2,4),(1,3,5),(1,-2,3)\) and \((6, \mathrm{k}, 2)\) are coplanar, then \(\mathrm{k}=\)
- A -5
- B 4
- C -3
- D 1
Answer & Solution
Correct Answer
(C) -3
Step-by-step Solution
Detailed explanation
\(\vec{AB} = (1-6, 3-2, 5-4) = (-5, 1, 1)\) \(\vec{AC} = (1-6, -2-2, 3-4) = (-5, -4, -1)\) \(\vec{AD} = (6-6, k-2, 2-4) = (0, k-2, -2)\) \(\begin{vmatrix} -5 & 1 & 1 \\ -5 & -4 & -1 \\ 0 & k-2 & -2 \end{vmatrix} = 0\) \(-5(8+k-2) - 1(10-0) + 1(-5(k-2)-0) = 0\)…
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