Correct Answer – B
Any vector coplanar with vectors ` hati + hatj and hatj + hatk ` is
`a=x (hati +hatj )+y (hatj +hatk)`
`implies a=xhati +(x+y)hatj +yhatk`
It is given that a is paraallel to ` 2 hati – 2 hatj – 4 hatk `
` therefore a= lamda ( 2 hati – 2hatj – 4 hatk )` for some scalar ` lamda `.
`implies [ x hati +(x+y) hatj +yhatk ]= lamda (2 hati – 2hatj – 4 hatk)`
`implies x= 2 lamda , x+y=- 2 lamda and y=- 4 lamda `
`implies x=2lamda and y=-4 lamda `
`therefore a= 2 lamda ( hati – hatj – 2hatk )` , where `lamda in R.`