The line passing through the points `(5,1,a)` and `(3,b,1)` crosses the yz-plane at the point `(0,17/2,(-13)/2)`.Then

Options

A. `a=8,b=2`
B. `a=2,b=8`
C. `a=4,b=6`
D. `a=6,b=4`

Answer

D

Explanation

Equation of line passing through `(5,1,a)` and `(3,b,1)` is
`(x-3)/(5-3)=(y-b)/(1-b)=(z-1)/(a-1)`…………….i
As point `(0, 17/2, (-13)/2)` satisfies
Eq. i we get
`-3/2=(17/2-b)/(1-b)=(-13/2-1)/(a-1)`
From Ist and IIIrd terms
`a-1=((-15/2))/((-3/2))impliesa=6`
From Ist and IInd terms
`-3(1-b)=2(17/2-b)impliesb=4`