The line passing through the points (5,1,6) and (3,4,1) is given as

      (x-5)/(3-5) = (y-1)/(4-1) = (z-6)/(1-6)

=> (x-5)/(-2) = (y-1)/3 = (z-6)/(-5) = k(say)

=> (x-5)/(-2) = k

=> x - 5 = -2k

=> x = 5 - 2k

    (y-1)/3 = k

=> y - 1 = 3k

=> y = 3k + 1

and (z-6)/(-5) = k

=> z - 6 = -5k

=> z = 6 - 5k

Now, any point on the line is of the form (5 - 2k, 3k + 1, 6 - 5k)

The equation of YZ-plane is x = 0

Since the line passes through YZ-plane

So, 5 - 2k = 0

=> k = 5/2

Now, 3k + 1 = 3 * 5/2 + 1 = 15/2 + 1 = 17/2

and 6 - 5k = 6 - 5*5/2 = 6 - 25/2 = -13/2

Hense, the required point is (0, 17/2, -13/2)