Find the coordinates of the points which tris | vedclass

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Question

(A) Let $A$ and $B$ be the points that trisect the line segment joining points $P(4, 2, -6)$ and $Q(10, -16, 6)$.Point $A$ divides $PQ$ in the ratio $

Vedclass · Accepted Answer

$(6, -4, -2)$ and $(8, -10, 2)$

Vedclass · Answer

(A) Let $A$ and $B$ be the points that trisect the line segment joining points $P(4, 2, -6)$ and $Q(10, -16, 6)$.Point $A$ divides $PQ$ in the ratio $1:2$. Therefore,by the section formula,the coordinates of point $A$ are given by:$A = \left(\frac{1(10) + 2(4)}{1 + 2}, \frac{1(-16) + 2(2)}{1 + 2}, \frac{1(6) + 2(-6)}{1 + 2}\right) = \left(\frac{18}{3}, \frac{-12}{3}, \frac{-6}{3}\right) = (6, -4, -2)$Point $B$ divides $PQ$ in the ratio $2:1$. Therefore,by the section formula,the coordinates of point $B$ are given by:$B = \left(\frac{2(10) + 1(4)}{2 + 1}, \frac{2(-16) + 1(2)}{2 + 1}, \frac{2(6) + 1(-6)}{2 + 1}\right) = \left(\frac{24}{3}, \frac{-30}{3}, \frac{6}{3}\right) = (8, -10, 2)$Thus,the coordinates of the points are $(6, -4, -2)$ and $(8, -10, 2)$.

Find the coordinates of the points which trisect the line segment joining the points $P(4, 2, -6)$ and $Q(10, -16, 6)$.

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