Question:
16. Find the coordinates of the point P which is five-sixth of the way from A(2, 3, –4) to B(8, –3, 2).
Answer:
Given points are: A(2, 3, –4), B(8, –3, 2)
Let P(x, y, z) be the required point.
Given P divides AB in the ratio 5 : 1
So, P(x, y, z) = {(5*8 + 1*2)/(5 + 1), (-3*5 + 1*3)/(5 + 1), (5*2 + -4*1)/(5 + 1)}
=> P(x, y, z) = {(40 + 2)/6, (-15 + 3)/6, (10 - 4)/6}
=> P(x, y, z) = {42/6, -12/6, 6/6}
=> P(x, y, z) = {7, -2, 1}
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