Question

If $A=(2,-4,3),B=(1,3,-1)$ are two points, then the point of intersection of $AB$ and $xy$-plane is

• A. $(1,-7,4)$
• B. $\left(\frac{5}{2},\frac{5}{2},0\right)$
• C. $\left(\frac{5}{4},\frac{5}{4},0\right)$
• D. $(5,5,0)$

Answer 1

The correct option is C $\left(\frac{5}{4},\frac{5}{4},0\right)$

Line $AB:\frac{x-2}{-1}=\frac{y+4}{7}=\frac{z-3}{-4}$
Any point $C$ lying on the line $AB$ can be written as $(2-k,-4+7k,3-4k)$.
Since $C$ lies on $xy$ plane, $\Rightarrow 3-4k=0$
i.e. $k=\frac{3}{4}$
Hence, the point is $(\frac{5}{4},\frac{5}{4},0)$