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 may be

Engineering

Mathematics

Section Formulae and Centres of a Triangle

theorem in space

Distance from a Plane

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 $(\frac{a}{b}, \frac{p}{q})$ may be

$\frac{23}{12}$

$\frac{7}{5}$

$\frac{7}{12}$

$\frac{21}{10}$

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

According to the section formula

0 = \frac{- 4 a + 5 b}{a + b}

{for z co-cordinates}

⇒ 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{2 q + 3 p}{p + q}

∴ \frac{p}{q} = \frac{- 2}{3}

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

Option C should be correct