Question:
A plane bisects the line segment joining the points (1, 2, 3) and (-3, 4, 5) at right angles. Then this plane also passes through the point :
A plane bisects the line segment joining the points (1, 2, 3) and (-3, 4, 5) at right angles. Then this plane also passes through the point :
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The plane passes through the midpoint of the segment and has the segment as its normal direction.
Updated On: Nov 11, 2026
- \((-3,2,1)\)
- \((3,2,1)\)
- \((-1,2,3)\)
- \((1,2,-3)\)
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The Correct Option is A
Solution and Explanation
Midpoint of (1, 2, 3) and (-3, 4, 5) is (-1, 3, 4). Normal direction = (1+3, 2-4, 3-5) = (4, -2, -2), i.e. (2, -1, -1).
Plane: \(2(x+1)-(y-3)-(z-4)=0\Rightarrow 2x-y-z+9=0\).
Check (-3, 2, 1): \(-6-2-1+9=0\). Satisfied. Check (3, 2, 1): 6-2-1+9 = 12, no. (-1, 2, 3): -2-2-3+9 = 2, no. (1, 2, -3): 2-2+3+9 = 12, no.
Answer: (1) (-3, 2, 1)
Plane: \(2(x+1)-(y-3)-(z-4)=0\Rightarrow 2x-y-z+9=0\).
Check (-3, 2, 1): \(-6-2-1+9=0\). Satisfied. Check (3, 2, 1): 6-2-1+9 = 12, no. (-1, 2, 3): -2-2-3+9 = 2, no. (1, 2, -3): 2-2+3+9 = 12, no.
Answer: (1) (-3, 2, 1)
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