If `2(y-a)` is the harmonic mean between `y-x` and `y-z` then `x-a, y—a` and `z-a` are in

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

If, for positive real numbers x, y, z, the numbers x+y, 2y and y + z are in harmonic progression, then which one of the following is correct ?

Find the angle between the lines x-2y+z=0=x+2y-2z and x+2y+z=0=3x+9y+5z

The shortest distance between the lines 2x+y+z-1=0=3x+y+2z-2 and x=y=z, is

The mean of x, y , z is y , then x + z = 2y . (True / False)

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 .