Find the equation of the plane which bisects the line joining (-1,2,3) and (3,-5,6) at right angle.
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Let A(-1,2,3) & B(3,-5,6) be the given points and C Is the mid point of AB.
∴ C is [ -1+3/2 , 2 - 5/2 , 3 + 6/2]
=> [ 1, -3/2 + 9/2 ]
Since , the line passes through the point is
=> [ 1,-3/2 +9/2]
∴ Equation of plane is
A(x - 1) + B [v +3/2] + C [ z - 9/2]= 0 --(1)
Direction ratio.of AB are 3+1 , -5 -2, 6 -3, 4 -7,3.
∴The line with direction ratios 4,-6,-3 is normal to the plane (1)
∴ 4 (x -1) -7 [ v + 3/2] +3 [ z -9/2 ] = 0
∴ 4x - 4 - 7v + 21/2 + 3x - 27/2 = 0
∴ 4x - 7v +3z - 28 = 0
It is the required equation
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