Question

If $A=(1,2,3),B=(2,3,4)$ and $AB$ is produced upto $C$ such that $2AB=BC$, then $C=$

• A. $(5,4,6)$
• B. $(6,2,4)$
• C. $(4,5,6)$
• D. $(6,4,5)$

Answer 1

Answer: (C)

$(4,5,6)$

Let the point $C$ be $(i,j,k)$.
Since, $B$ divides $AC$ in the ratio $1:2$
Coordinates of $B$ should be $(\frac{2+i}{3},\frac{4+j}{3},\frac{k+6}{3})$
Comparing the values given already for $B$, we get,

$i=4$, $j=5$ and $k=6$