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$A = (2, 4, 5)$ and $B = (3, 5, - 4)$ are two points. If the $x y -$ plane, $x z -$ plane divides AB in the ratio $a : b, p : q$ respectively then $\frac{a}{b} - \frac{p}{q} =$

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$\frac{23}{12}$

$\frac{9}{20}$

$\frac{7}{12}$

$\frac{41}{20}$

answer is D.

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Detailed Solution

$A = (2, 4, 5) B = (3, 5, - 4) a : b = - z_{1} : z_{2} = - 5 : - 4 = 5 : 4 p : q = - y_{1} : y_{2} = - 4 : 5 \frac{a}{b} - \frac{p}{q} = \frac{5}{4} + \frac{4}{5} = \frac{41}{20}$

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