AP EAMCET · Maths · Three Dimensional Geometry
Let the plane \(a x+b y+c z+d=0\) bisect the line joining the points \((4,-3,1)\) and \((2,3,-5)\) at the right angles. If \(a, b, c, d\) are integers, then the minimum value of \(\left(a^2+b^2+c^2+d^2\right)\) is
- A \(14\)
- B \(28\)
- C \(20\)
- D \(30\)
Answer & Solution
Correct Answer
(B) \(28\)
Step-by-step Solution
Detailed explanation
Step-1 Using mid point concept: Given that the equation of the plane is \(a x+b y+c z+d=0\) and the line passed the plane having the coordinates as \(P(4,-3,1)\) and \(Q(2,3,-5)\). Let \(M(x, y, z)\) be the mid-point of the line passing through the plane. Using the mid-point…
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