InterviewSolution
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InterviewSolution
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Find the ratio in which the line segment, joining the points, `P(2,3,4) and Q(-3,5,-4)` is divided by the yz-plane. Also, find the points of intersection. |
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Answer» Let PQ be the divided by the zy-plane at a point R in the ratio `lambda:1`. Then, the coordinate of R are `((-3lambda+2)/(lambda+1),(5lambda+3)/(lambda+1),(-4lambda+4)/(lambda+1))` Since R lies on the yz-plane, the x-coordinate or R is thereofore, 0. `:. (-3lambda+2)/(lambda+1)=0, or lambda=(2)/(3)` So, the required ratio is `(2)/(3) : 1,i.e., 2:3` Putting `lambda=(2)/(3)` in (i), the point of intersection of the line segment PQ any the yz- plane is `(0,(19)/(5),(4)/(5))` |
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