Which one of the following gives the coordinates of the point that divides the line…

MATHEMATICS · Single correct · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry

Problem

Which one of the following gives the coordinates of the point PP that divides the line segment joining A(x1,y1,z1)A(x_1,y_1,z_1) and B(x2,y2,z2)B(x_2,y_2,z_2) internally in the ratio m:nm:n? (a) (nx2+mx1m+n,  ny2+my1m+n,  nz2+mz1m+n)\left(\dfrac{n x_2 + m x_1}{m+n},\; \dfrac{n y_2 + m y_1}{m+n},\; \dfrac{n z_2 + m z_1}{m+n}\right) (b) (mx2+nx1m+n,  my2+ny1m+n,  mz2+nz1m+n)\left(\dfrac{m x_2 + n x_1}{m+n},\; \dfrac{m y_2 + n y_1}{m+n},\; \dfrac{m z_2 + n z_1}{m+n}\right) (c) (mx1+nx2m+n,  my1+ny2m+n,  mz1+nz2m+n)\left(\dfrac{m x_1 + n x_2}{m+n},\; \dfrac{m y_1 + n y_2}{m+n},\; \dfrac{m z_1 + n z_2}{m+n}\right) (d) (mx1+nx2m−n,  my1+ny2m−n,  mz1+nz2m−n)\left(\dfrac{m x_1 + n x_2}{m-n},\; \dfrac{m y_1 + n y_2}{m-n},\; \dfrac{m z_1 + n z_2}{m-n}\right)

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