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(\right. \frac{a}{b} , \frac{p}{q} \left.\right) may be

Engineering

Mathematics

Line of Greatest Slope

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}

\Rightarrow 5 b = 4 a

\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

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