If `x + y + z = 6` and `3^x = 5^y = 15^-z,` then find `x^2 + y^2 +z^2 `

2x + 3y-5z = 7, x + y + z = 6,3x-4y + 2z = 1, then x =

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

Find the angle between the planes : (i) 3 x - 6y - 2z = 7 " " 2x + y - 2z = 5 (ii) 4 x + 8y + z = 8 " " and y + z = 4 (iii) 2 x - y + z =6 " " and x + y + 2z = 7 .

Add: 5x - 8y + 2z, 3z - 4y - 2x, 6y - z - x and 3x - 2z - 3y

Prove that the lines 3x + 2y + z – 5 = 0 = x + y – 2z – 3 and 2x – y – z = 0 = 7x + 10y – 8z – 15 are perpendicular

If x,y,z, in R such that x+y+z=4, x^2+y^2+z^2=6 then find the range of x.

Find x ,\ y and z so that A=B , where A=[x-2 3 2z 18 z y+2 6z] , B=[y z6 6y x2y]

Prove that Det [[x + y + 2z, x, y], [z, y + z + 2x, y], [z, x, z + x + 2y]] = 2 (x + y + z) ^ 3

What should be added to x y+y z+z x to get x y-y z-z x ? -2x y-2y z-2z x (b) -3x y-y z-z x -3x y-3y z-3z x (d) 2x y+2y z+2z x