If the line joining A(1, 3, 4) and B is divid | vedclass

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(A) Let the coordinates of point $B$ be $(x, y, z)$.Using the section formula for internal division, the point $P$ dividing the line segment $AB$ in t

Vedclass · Accepted Answer

$(-11, 3, 8)$

Vedclass · Answer

(A) Let the coordinates of point $B$ be $(x, y, z)$.Using the section formula for internal division, the point $P$ dividing the line segment $AB$ in the ratio $m:n = 1:3$ is given by:$P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n} ight)$Substituting the given values:$(-2, 3, 5) = \left( \frac{1 	imes x + 3 	imes 1}{1+3}, \frac{1 	imes y + 3 	imes 3}{1+3}, \frac{1 	imes z + 3 	imes 4}{1+3} ight)$$(-2, 3, 5) = \left( \frac{x+3}{4}, \frac{y+9}{4}, \frac{z+12}{4} ight)$Equating the coordinates:$1) \frac{x+3}{4} = -2 \Rightarrow x+3 = -8 \Rightarrow x = -11$$2) \frac{y+9}{4} = 3 \Rightarrow y+9 = 12 \Rightarrow y = 3$$3) \frac{z+12}{4} = 5 \Rightarrow z+12 = 20 \Rightarrow z = 8$Thus, the coordinates of $B$ are $(-11, 3, 8)$.

If the line joining $A(1, 3, 4)$ and $B$ is divided by the point $P(-2, 3, 5)$ in the ratio $1: 3$, then the coordinates of $B$ are:

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