MHT CET · Maths · Three Dimensional Geometry
The distance of the point \((5,3,-1)\) from the plane passing through points \((2,1,0),(3,-2,4)\) and \((1,-3,3)\) is
- A \(\frac{2}{\sqrt{3}}\) units
- B \(\frac{4}{\sqrt{3}}\) units
- C \(\sqrt{3}\) units
- D \(\frac{1}{\sqrt{3}}\) units
Answer & Solution
Correct Answer
(A) \(\frac{2}{\sqrt{3}}\) units
Step-by-step Solution
Detailed explanation
Plane vectors: \(\vec{u} = (3-2, -2-1, 4-0) = (1, -3, 4)\), \(\vec{v} = (1-2, -3-1, 3-0) = (-1, -4, 3)\) Normal vector: \(\vec{n} = \vec{u} \times \vec{v} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & -3 & 4 \\ -1 & -4 & 3 \end{vmatrix} = (7, -7, -7)\), simplified to \((1, -1, -1)\)
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