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JEE Mains · Maths · STD 12 - 10. vector algebra
The foot of perpendicular from the origin \(O\) to a plane \(P\) which meets the co-ordinate axes at the points \(A, B, C\) is \((2, a, 4), a \in N\). If the volume of the tetrahedron \(OABC\) is \(144\) unit \(^3\), then which of the following points is \(NOT\) on \(P\) ?
- A \((2,2,4)\)
- B \((0,4,4)\)
- C \((3,0,4)\)
- D \((0,6,3)\)
Answer & Solution
Correct Answer
(C) \((3,0,4)\)
Step-by-step Solution
Detailed explanation
Equation of Plane: \((2 \hat{i}+a \hat{j}+4 \hat{ k }) \cdot[( x -2) \hat{ i }+( y - a ) \hat{ j }+( z -4) \hat{ k }]=0\) \(\Rightarrow 2 x + ay +4 z =20+ a ^2\) \(\Rightarrow A \equiv\left(\frac{20+ a ^2}{2}, 0,0\right)\) \(B \equiv\left(0, \frac{20+ a ^2}{ a }, 0\right)\)…
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