Question

If the point $A(3,-2,4),B(1,1,1)$ and $C(-1,4,-2)$ are collinear then $(CA:AB)=$

• A. $1:2$
• B. $-2:1$
• C. $2:3$
• D. $2:1$

Answer 1

The correct option is B $-2:1$

The point $P(x,y,z)$ divides line joining $A(x_1,y_1,z_1),B(x_2,y_2,z_2)$ in the ratio $x_1-x:x-x_2$ or $y_1-y:y-y_2$ or $z_1-z:z-z_2$
$\therefore$ The point $A(3,-2,4)$ divides line joining $C(-1,4,-2),B(1,1,1)$ in the ratio $-1-3:3-1=-2:1$