If the lines ` x = 1 + s, y = - 3 - lamda s , z = 1 + lamda s and x = ( t ) / ( s ) , y = 1 + t , z = 2 - t ` are coplanar, then ` lamda ` is equal to

Options

A. ` - 2 `
B. `- 1 `
C. ` - ( 1 ) / ( 2 ) `
D. 0

Answer

A

Explanation

Given, line are ` ( x - 1 ) / ( 1 ) = ( y + 3 ) / ( - lamda ) = ( z - 1) / ( lamda ) `
and ` ( x ) / ( 1//2 ) = ( y - 1 ) / ( 1 ) = ( z - 2 ) / ( - 1 ) `
If lines are coplanar, then
` |{:( 1-0, -3-1,1-2 ) , ( 1, - lamda, lamda ), ( 1, 2, 2 ) :}| = 0 `
` rArr |{:( 1 , - 4, - 1 ) , ( 1, - lamda,lamda ) , ( 1, 2, - 2) :}| = 0 rArr lamda = - 2 `