If A(1, 2, -1) and B(-1, 0, 1) are given,then | vedclass

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Question

(A) The coordinates of a point $P$ dividing the line segment joining $A(x_1, y_1, z_1)$ and $B(x_2, y_2, z_2)$ externally in the ratio $m:n$ are given

Vedclass · Accepted Answer

$(3, 4, -3)$

Vedclass · Answer

(A) The coordinates of a point $P$ dividing the line segment joining $A(x_1, y_1, z_1)$ and $B(x_2, y_2, z_2)$ externally in the ratio $m:n$ are given by the formula: $P = \left( \frac{mx_2 - nx_1}{m - n}, \frac{my_2 - ny_1}{m - n}, \frac{mz_2 - nz_1}{m - n} \right)$ Given $A(1, 2, -1)$,$B(-1, 0, 1)$,$m = 1$,and $n = 2$. Substituting the values: $x = \frac{1(-1) - 2(1)}{1 - 2} = \frac{-1 - 2}{-1} = \frac{-3}{-1} = 3$ $y = \frac{1(0) - 2(2)}{1 - 2} = \frac{0 - 4}{-1} = \frac{-4}{-1} = 4$ $z = \frac{1(1) - 2(-1)}{1 - 2} = \frac{1 + 2}{-1} = \frac{3}{-1} = -3$ Thus,the coordinates of $P$ are $(3, 4, -3)$.

If $A(1, 2, -1)$ and $B(-1, 0, 1)$ are given,then the coordinates of point $P$ which divides the line segment $AB$ externally in the ratio $1:2$ are:

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