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 the line passing through (5, 1, a ) and ` ( 3, b , 1 ) ` is
` ( x - 3 ) / ( 5 - 3 ) = ( y - b ) / ( 1 - b ) = ( z - 1 ) / ( a - 1 ) `
` rArr ` Point ` ( 0 , ( 17 ) / ( 2 ) , - ( 13 )/ (2 )) ` satisfying Eq. (i) , we get
` therefore - ( 3 )/ ( 2 ) = ((17 ) / ( 2) - b ) / ( 1 - b ) = ( - ( 13 ) / ( 2 ) - 1 ) / ( a - 1 ) `
`rArr a - 1 = (( - ( 15 ) / ( 2))) / (( - (3 ) / ( 2 ) ) ) = 5 rArr a = 6 `
Also, ` - 3 ( 1 - b ) = 2 ( ( 17 ) / (2 ) - b ) `
` rArr 3b - 3 = 17 - 2b `
`rArr 5 b = 20 `
` rArr b = 4 `