Answer
See explanation
Work Step by Step
(a) The distance from a point to the ∞y-plane is the absolute value of the -coordinate of the point. Thus, the distance
is 6 = 6.
(b) Similarly, the distance to the y›-plane is the absolute value of the x-coordinate of the point: 4 = 4.
(c)The distance to the ∞z-plane is the absolute value of the y-coordinate of the point:$ - 2 = 2$.
(d) The point on the x-axis closest to (4, -2, 6) is the point (4, 0, 0). (Approach the x-axis perpendicularly.)
The distance from (4, -2, 6) to the x-axis is the distance between these two points:
(4,-2,6) and (4,0,0):
$\sqrt{(-2)^2+6^2}=2\sqrt{10}$
(e) The point on the y-axis closest to (4, -2, 6) is (0, -2, 0). The distance between these points is $\sqrt{4^2+6^2}=2\sqrt{13}$.
(f) The point on the z-axis closest to (4, -2, 6) is (0, 0, 6). The distance between these points is $\sqrt{4^2+(-2)^2}=2\sqrt 5$
