The value of `{(x-y)^3+(y-z)^3+(z-x)^3}/{9(x-y)(y-z)(z-x)} `
(1) `0`
(2) `1/9`
(3) `1/3`
(4) `1`

Write the value of |(x+y,y+z,z+x),(z,x,y),(-3,-3,-3)|

evaluate: |(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z)|

Prove that : |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|=(x-y)(y-z)(z-x)(x+y+z)

The lines x/1=y/2=z/3 and (x-1)/(-2)=(y-2)/(-4)=(z-3)/(-6) are

Verify that x3+y3+z3-3xyz=1/2(x+y+z)[(x-y)2+(y-z)2+(z-x)2]

Prove that : |{:(1,x,x^(3)),(1,y,y^(3)),(1,z,z^(3)):}| =(x-y)(y-z)(z-x)(x+y+z)

If {:[(x+y,y-z),(z-2x,y-x)]:}={:[(3,-1),(1,1)]:} , then

The lines (x-1)/1=(y-2)/2=(z-3)/(3) and (x-1)/1=y/3 =z/4 are

Equation of theine passing through hati+hatj-3hatk and perpendiculr to the plane 2x-4y+3z+5=0 is (A) (x-1)/2=(1-y)/(-4)=(z-3)/3 (B) (x-1)/2=(1-y)/4=(z+3)/3 (C) (x-2)/1=(y+4)/1)=(z-3)/3 (D) (x-1)/(-2)=(1-y)/(-4)=(z-3)/3

The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z+3=0 is the line (1) (x+3)/3=(y-5)/1=(z-2)/(-5) (2) (x+3)/(-3)=(y-5)/(-1)=(z+2)/5 (3) (x-3)/3=(y+5)/1=(z-2)/(-5) (3) (x-3)/(-3)=(y+5)/(-1)=(z-2)/5