+3=6+2zquad " 5."quad 2x-1=14-x

The lines x + y + z - 3 = 0 = 2x - y + 5z - 6 and x - y - z + 1 = 0 = 2x + 3y + 7z - k are coplanar then k equals

The equation of the plane passing through the point 1,1,1) and perpendicular to the planes 2x+y-2z=5a n d3x-6y-2z=7, is 14 x+2y+15 z=3 14 x+2y-15 z=1 14 x+2y+15 z=31 14 x-2y+15 z=27

The equations 2x-3y+6z=4, 5x+7y-14z=1 3x+2y-4z=0, have

Show that each of the following systems of linear equations is consistent and also find their solutions: 6x+4y=2 9x+6y=3 2x+3y=5 6x+9y=15 5x+3y+7z=4 3x+26 y+2z=9 7x+2y+10 z=5 x-y+z=3 2x+y-z=2 -x-2y+2z=1 x+y+z=6 x+2y+3z=14 x+4y+7z=30 2x+2y-2z=1 4x+4y-z=2 6x+6y+2z=3

If the lines (1 -x )/(3) = ( 7y - 14)/(2 lamda) = (z - 3)/(2) "and" (7 - 7x)/(3lamda) = (y - 5)/(1) = ( 6 - z ) /(5) are at right angle, then the value of lamda is

Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .

Add 2x - 3y + z , 5y - x + 7z and 3x - y - 6z.

The distance between the planes 3x+2y-6z=14=0 and 3x+2y-6z+21=0 is