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

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Question

(A) Let the coordinates of point $B$ be $(x, y, z)$.Given that point $P(-2, 3, 5)$ divides the line segment joining $A(1, 3, 4)$ and $B(x, y, z)$ in t

Vedclass · Accepted Answer

$(-11,3,8)$

Vedclass · Answer

(A) Let the coordinates of point $B$ be $(x, y, z)$.Given that point $P(-2, 3, 5)$ divides the line segment joining $A(1, 3, 4)$ and $B(x, y, z)$ in the ratio $m:n = 1:3$.Using the section formula for internal division:$P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n} \right)$Substituting the values:$(-2, 3, 5) = \left( \frac{1(x) + 3(1)}{1+3}, \frac{1(y) + 3(3)}{1+3}, \frac{1(z) + 3(4)}{1+3} \right)$$(-2, 3, 5) = \left( \frac{x+3}{4}, \frac{y+9}{4}, \frac{z+12}{4} \right)$Equating the coordinates:$1) \frac{x+3}{4} = -2 \Rightarrow x+3 = -8 \Rightarrow x = -11$$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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