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Question
Find the distance from (4, - 2, 6) to each of the following:
(a) The XY-plane
(b) The YZ-plane
(c) The XZ-plane
(d) The X-axis
(e) The Y-axis
(f) The Z-axis.
Solution
Let the point A be (4, - 2, 6).
Then,
(a) The distance of A from XY-plane = |z| = 6
(b) The distance of A from YZ-plane = |x| = 4
(c) The distance of A from ZX-plane = |y| = 2
(d) The distance of A from X-axis
`= sqrt("y"^2 + "z"^2) = sqrt((-2)^2 + 6^2) = sqrt40 = 2sqrt10`
(e) The distance of A from Y-axis
`sqrt("z"^2 + "x"^2) = sqrt(6^2 + 4^2) = sqrt52 = 2sqrt13`
(f) The distance of A from Z-axis
`= sqrt("x"^2 + "y"^2) = sqrt(4^2 + (-2)^2) = sqrt20 = 2sqrt5`
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