What are the intercepts of 7x+2y-14z=56 a. (8,0,0) (0,-28,0) (0,0,-4) b. (8,0,0) (0,28,0) (0,0,-4) c. (8,0,0) (0,28,0) (0,0,4) d. (8,0,0) (0,-28,0) (0,0,4)

Since the equation is in 3 variables, there will be 3 intercepts:

1) x-intercept
Where y and z coordinate are zero.
So, we can say
7x + 2(0)-14(0) = 56
So, x = 8 is the x-intercept

2) y-intercept
where x and z coordinate are zero
So, we can write
7(0) + 2y - 14(0) = 56
So, y = 28 is the y-intercept

3) z-intercept
where x and y coordinates are zero
So, we can write
7(0)+2(0)-14z=56
So, z=-4 is the z intercept

Therefore, the correct answer to this question is option B

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.