Question

Let $A=(2,3,-1)$, $B=(1,-1,2)$. A point $C$ on the $y$-axis such that $AB\perp BC$ has the coordinates:

• A. $(-\frac{9}{4},0,\frac{-9}{4})$
• B. $(0,-\frac{4}{9},0)$
• C. $(0,\frac{-9}{4},0)$
• D. $(0,\frac{9}{4},0)$

Answer 1

The correct option is C $(0,\frac{-9}{4},0)$

Let the point $C$ is $(0,b,0)$.

The vector $AB$ is given by $-i-4j+3k$ and vector $BC$ is given by $-i+(b+1)j-2k$.

Since, $AB\perp BC$, so their dot product is zero.

$\Rightarrow 1-4(b+1)-6=0$

$\Rightarrow b=\frac{-9}{4}$

Hence, $C=(0,\frac{-9}{4},0)$