If the line passes through the point P(6,-1,2), Q(8,-7,`2lamda`) and R(5,2,4) then value of `lamda` is . . .

Options

A. `-3`
B. `0`
C. `-1`
D. `2`

Answer

C

Explanation

Equation of the line passes through the points P(6,-1,2) and Q(8,-7,`2lamda`)
`implies(x-6)/(8-6)=(y+1)/(-7+1)=(z-2)/(2lamda-2)`
`implies(x-6)/(2)=(y+1)/(-6)=(z-2)/(2lamda-2)`
Line (i) passes through point R(5,2,4)
`therefore(5-6)/(2)=(2+1)/(-6)=(4-2)/(2lamda-2)`
`implies-(1)/(2)=(3)/(-6)=(2)/(2lamda-2)`
`implies-(1)/(2)=(3)/(-6)=(2)/(2lamda-2)`
`implies(2)/(2lamda-2)=-(1)/(2)implies(1)/(lamda-1)=-(1)/(2)`
`implieslamda-1=-2`
`implieslamda=-1`