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Question
P is a point on the line joining the points A(0, 5, −2) and B(3, −1, 2). If the x-coordinate of P is 6, then its z-coordinate is ______.
Options
10
6
–6
–10
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Solution
P is a point on the line joining the points A(0, 5, −2) and B(3, −1, 2). If the x-coordinate of P is 6, then its z-coordinate is 6.
Explanation:
The line through the points (0, 5, −2) and (3, −1, 2) is `x/(3 - 0) = (y - 5)/(-1 - 5) = (z + 2)/(2 + 2)`
or, `x/3 = (y - 5)/(-6) = (z + 2)/4`
Any point on the line is (3k, −6k + 5, 4k − 2), where k is an arbitrary scalar.
3k = 6
⇒ k = 2
The z-coordinate of the point P will be 4 × 2 − 2 = 6.
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