If `x = sinAcosB` and `y = sinAsinB` and `z= cosA` then find `x^2+y^2+z^2`

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

If x,y,z are positive intergers and x+y+z=240 and x^2 + y^2= z^2 then find the number of positive solutions.

If (x + y)/2 = (y+z)/3 = (z + x)/4 , then find x : y: z .

If 2x = 3y = 4z, find x:y: z.

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 .

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.

Let's find value of : (x - y)a + (y - z) b + (z -x)c if a = x^2 + xy + y^2,b = y^2 + yz + z^2, c = z^2 + zx + x^2