Question

$A=(2,4,5)\text{and}B=(3,5,-4)$ are two points. If the $xy-$plane, $yz-$plane divide $AB$ internally and externally in the ratios $a:b$ 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

The correct option is C $\frac{7}{12}$

Given: points are $A(2,4,5)$ and $B(3,5,-4)$.
$XY$ plane divides $AB$ internally and $Z$-coordinate zero ,
Using Section formula
$0=\frac{m{z}_2+n{z}_1}{m+n}$
$0=\frac{a(-4)+b\left(5\right)}{a+b}$
$\frac{a}{b}=\frac{5}{4}\cdots \left(i\right)$
$YZ$ plane divides $AB$ externally and $X$-coordinate zero ,
Using Section formula
$0=\frac{m{x}_2-n{x}_1}{m-n}$
$0=\frac{p\left(3\right)-q\left(2\right)}{p-q}$
$\frac{p}{q}=\frac{2}{3}\cdots \left(ii\right)$
From equation $\left(i\right),\left(ii\right)$
$\therefore \frac{a}{b}-\frac{p}{q}=\frac{5}{4}-\frac{2}{3}=\frac{15-8}{12}=\frac{7}{12}$