Find the value of `lambda` such that the lines `(x-2)/6=(y-1)/lambda=(z+5)/(-4)` is perpendicular to the plane `3x-y-2z=7.`

Find the value of lambda such that the line (x-2)/6=(y-1)/lambda=(z+5)/4 is perpendicular to the planes 3x-y+2z=7 .

Find the value of lambda for which the planes 2x-4y+3z=7 and x+2y+lambdaz=18 are perpendicular to each other.

Find the value of lambda for which the line (x-1)/2=(y-1)/3=(z-1)/lambda is parallel to the plane vecr.(2hati+3hatj+4hatk)=4 .

Find the value of lambda for which the planes x-4y+lambdaz+3=0 and 2x+2y+3z=5 are perpendicular to each other.

Find the value of 'lambda' so the lines: (1-x)/(3) = (7y -14)/(lambda) = (z-3)/(2) and (7 - 7x)/(3 lambda) = (y -5)/(1 ) = (6 - z)/(5) are at right angles. Also, find whether the lines are ntersecting or not .

Prove that the plane 2x+3y-4z=9 is perpendicular to each of the planes x+2y+2z-7=0 and 5x+6y+7z=23 .

Find the value of lambda so that the following lines are perpendicular to each other.(x-5)/(5 lambda+2)=(2-y)/(5)=(1-z)/(-1),(x)/(1)=(2y+1)/(4 lambda)=(1-z)/(-3)

(i) Find the equation of the plane passing through (1,-1,2) and perpendicular to the planes : 2 x + 3y - 2z = 5 , x + 2y - 3z = 8 . (ii) find the equation of the plane passing through the point (1,1,-1) and perpendicular to each of the planes : x + 2y + 3z - 7 = 0 and 2x - 3y + 4z = 0 . (iii) Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to the planes : 3x + 2y - 3z = 1 and 5x - 4y + z = 5.

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0