What are the intercepts of 7x plus 2y - 14z equals 56?

To find the intercepts of the equation (7x + 2y - 14z = 56), we determine where the equation intersects the axes.

1. For the x-intercept, set (y = 0) and (z = 0):
   (7x = 56 \Rightarrow x = 8), so the x-intercept is ((8, 0, 0)).

2. For the y-intercept, set (x = 0) and (z = 0):
   (2y = 56 \Rightarrow y = 28), so the y-intercept is ((0, 28, 0)).

3. For the z-intercept, set (x = 0) and (y = 0):
   (-14z = 56 \Rightarrow z = -4), so the z-intercept is ((0, 0, -4)).

Thus, the intercepts are ((8, 0, 0)), ((0, 28, 0)), and ((0, 0, -4)).