Question

If xy -plane and yz-plane divides the line segment joining A(2,4,5) and B(3,5,-4) in the ratio a:b and p:q respectively then value of $\left(\frac{a}{b},\frac{p}{q}\right)$ may be

• A. $\frac{23}{12}$
• B. $\frac{7}{5}$
• C. $\frac{7}{12}$
• D. $\frac{21}{10}$

Answer 1

Answer: (C)

$\frac{7}{12}$

Let the co-ordinate of xy plane be $(x,y,0)$

According to the section formula

$0=\frac{-4a+5b}{a+b}$ {for z co-cordinates}

$\Rightarrow 5b=4a$

$\frac{a}{b}=\frac{5}{4}$

Let the co-ordinate of yz-plane be (0, y, z)

According to the section formula,

$0=\frac{2q+3p}{p+q}$

$\therefore \frac{p}{q}=\frac{-2}{3}$

$(\frac{a}{b}+\frac{p}{q})=(\frac{5}{4}-\frac{2}{3})=\left(\frac{15-8}{12}\right)=\frac{7}{12}$

Option C should be correct