The vectors `veca=xhati-2hatj+5hatj and vecb=hati+yhatj-zhatk` are collinear if (A) `x=1,y=-2,z=-5` (B) `x=1/2,y=-4,z=-10` (C) `x=-1/2,y=4,z=10` (D) none of these

Find the values of x,y and z so that vectors veca=xhati+4hatj+zhatk and vecb=3hati+yhatj+hatk are equal.

Find the values of x,y and z so that the vectors veca=xhati+2hatj+zhatk and vecb=2hati+yhatj+hatk are equal.

The image of plane 2x-y+z=2 in the plane mirror x+2y-z=3 is (a) x+7y-4x+5=0 (b) 3x+4y-5z+9=0 (c) 7x-y+2z-9=0 (d) None of these

Find the values of x and y so that the vector 3hati+4hatj and xhati+yhatj are equal.

A plane through the line (x-1)/1=(y+1)/(-2)=z/1 has the equation (A) x+y+z=0 (B) 3x+2y-z=1 (C) 4x+y-2z=3 (D) 3x+2y+z=0

If the vectors xhati+hatj+hatk,hati+yhatj+hatk and hati+hatj+zhatk are coplanar where, x ne1,y ne1 and z ne1 , then prove that (1)/(1-x)+(1)/(1-y)+(1)/(1-z)=1

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 line perpendicular to the plane 2x-y+5z=4 passing through the point (-1,0,1) is (A) (x+1)/2=-y=(z-1)/(-5) (B) (x+1)/(-2)=y=(z-1)/-5 (C) (x+1)/2=-y=(z-1)/5 (D) (x+1)/2=y=(z-1)/-5

The equation of a line 4x-4y-z+11=0=x+2y-z-1 can be put as (a)x/2=(y-2)/1=(z-3)/4 (b) (x-2)/2=(y-2)/1=z/4 (c) (x-2)/2=y/1=(z-3)/4 (d) None of these

Verify associativity of addition of rational i.e., (x+y)+z=x+(y+z), when: (i ) x=1/2, y=2/3,\ z=-1/5 (ii) x=(-2)/5, y=4/3,\ z=\ (-7)/(10)