Let A($\alpha$,4,7) and B(3,$\beta$,8) be two points in space. If YZ plane and ZX plane respectively divide the line segment joining the points A and B in the ratio 2:3 and 4:5, then the point C which divides AB in the ratio $\alpha:\beta$ externally is
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A useful shortcut: The ratio in which the xy-plane divides the line segment joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is $-z_1:z_2$. Similarly, for the yz-plane the ratio is $-x_1:x_2$, and for the xz-plane the ratio is $-y_1:y_2$.