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The line passing through the points (5, ...

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

A

`a=2,b=8`

B

`a=4,b=6`

C

`a=6,b=4`

D

`a=8,b=2`

Text Solution

Verified by Experts

The correct Answer is:
C
Equation of line passing through (5,1,a) and (3,b,1) is
`(x-3)/(5-3)=(y-b)/(1-b)=(z-1)/(z-1)` . . . . (i)
Point `(0,(17)/(2),-(13)/(2))` satisfies Eq. (i), we get
`-(3)/(2)=((17)/(2)-b)/(1-b)=(-(13)/(2)-1)/(a-1)`
`rArr" "a-1=((-(15)/(2)))/((-(3)/(2)))=5rArra=6`
Also `-3(1-b)=2((17)/(2)-b)rArr3b-3=17-2b`
`rArr" "5b=20rArrb=4`
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