`P=4x-z+3y`
`Q=-x+4z+3y`
Using the definitions above for P and Q. What is `2P-Q`?

If x^3 + y^3 + z^3 = 3(1 + xyz) , P = y + z - x, Q = z + x - y and R = x + y - z, then what is the value of P^3 + Q^3 + R^3- 3PQR ?

Let R = {(x,y): x, y in Z, y = 2x-4] . If (p,-2) and [4, q^(2))in R , then find the value of p and q

If (a-x)/(p x)=(a-y)/(q y)=(a-z)/(rz) and p ,q ,and r are in A.P., then prove that x ,y ,z are in H.P.

Let image of the line (x-1)/3=(y-3)/5=(z-4)/2 in the plane 2x-y+z+3=0 be Ldot A plane 7x+p y+q z+r=0 is such that it contains the line L and perpendicular to the plane 2x-y+z+3=0 then p=1 (b) q=42 p+q+r=30 (d) p+q+r=0

The sides of triangle are denoted by x , y nd z . Area of the triangle and semiperimeter of the triangle are denoted by P and q respectively .If P= sqrtq (q-x)(q-y)(q-z) and x+y-z=y+z-x=z+x-y=4 Find P (in square units)