Question

If the $XZ$-plane divides the straight line joining the points $(2,4,7)$ and $(3,-5,8)$ in the ratio $α:1$,then the value of $α$ is ?

• A. $\dfrac{5}{4}$
• B. $\dfrac{1}{3}$
• C. $\dfrac{7}{8}$
• D. $\dfrac{4}{5}$
• E. $\dfrac{5}{2}$

Answer 1

Answer: (D)

$\dfrac{4}{5}$

Answer 2

Given that

Let the $XZ$ plane divide the line segment joining points $(2,4,7)$ and $(3,−5,8)$ in the ratio $∝:1.$

Hence, by section formula, the coordinates of point of intersection are given by :

$(\dfrac{k(3)+2}{k+1}​,\dfrac{k(−5)+4}{k+1}​,\dfrac{k(8)+7​}{k+1})$

On the $XZ$ plane, the $y$-coordinate of any point is zero.

So

,$\dfrac{k(-5)+4}{k+1}=0$

⇒ $-5k+4=0$

⇒ $k=\dfrac{4}{5}$ (_Ans)