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Question

If the x-coordinate of a point P on the join of Q (2, 2, 1) and R (5, 1, −2) is 4, then its z-coordinate is
(a) 2
(b) 1
(c) −1
(d) −2

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Solution

c -1Suppose the point P divides the line joining the point Q 2, 2, 1 and R 5, 1, -2 in the ratio k:1.Using the section formula, the coordinates of the point of intersection are given byk5+2k+1, k1+2k+1, k-2+1k+1It is given that the X-coordinate of P is 4.k5+2k+1=45k+2=4k+1 k=2Now,Z-coordinate of P =k-2+1k+1 = 2-2+12+1 Substituting k=2 =-1

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