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The plane which bisects the line segment...

The plane which bisects the line segment joining the points (-3, -3, 4) and (3, 7, 6) at right angles, passes through which one of the following points?

A

(-2, 3, 5)

B

(2, 1, 3)

C

(4, 2, -1)

D

(4, -1, 7)

Text Solution

Verified by Experts

The correct Answer is:
C
Plane will pass through the mid-point of the given points
`therefore ` Plane will pass through (0, 2, 5). The normal vector of the plane will be along the line segment
`therefore vecn= 6hati+10htaj+2hatk " " therefore ` Equation of plane `6x+10y+2z=d`
Since it passes through (0,2,5)
`therefore 6(0)+10(2)+2(5)=d" " therefore ` Equation of plane `6x+10y+2z=30`
It passes through (4, 2, -1)
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