A vector coplanar with vectores ` hati + hatj and hatj + hatk ` and parallel to the vector ` 2 hati - 2 hatj - 4 hatk `is

Options

A. `hati - hatk`
B. `hati - hatj -2hatk `
C. `hati +hatj-hatk `
D. `3hati+3hatj-6hatk`

Answer

B

Explanation

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.`