Question

$A=(2,4,5)$ and $B=(3,5,-4)$ are two points. lf the $XY$-plane, $YZ$-plane divide $AB$ in the ratio $a:b$ and $p:q$ respectively, then $\frac{a}{b}+\frac{p}{q}=$

• A. $\frac{23}{12}$
• B. $\frac{-7}{12}$
• C. $\frac{7}{12}$
• D. $\frac{-22}{15}$

Answer 1

Answer: (C)

$\frac{7}{12}$

Given points are $A(2,4,5)$ and $B(3,5,-4)$.
Let the $XY$ plane divides the line $AB$ in the ratio $\lambda :1$.
Then the $z$ coordinate of $XY$ plane is zero.
$0=5-4\left(\lambda \right)$
$\lambda =\frac{5}{4}=\frac{a}{b}$
$YZ$ plane divides the line $AB$ such that x coordinate is zero.
$0=3\left(\alpha \right)+2$
$\alpha =\frac{-2}{3}=p:q$
Now, $\frac{a}{b}+\frac{p}{q}=\frac{5}{4}-\frac{2}{3}=\frac{7}{12}$

Hence, option C is correct.