Find λ, if the vectors →a = ^i + 3^j + ^k, →b = 2^i − ^j − ^k and →c = λ^j + 3^k are coplanar.

For the three vectors to be coplanar the volume of the parallelopiped formed by them should be zero, so (→a × →b) ⋅ →c = 0

⇒ | 1 3 1 |
| 2 -1 -1 | = 0
| 0 λ 3 |

= (1( -3 + λ) -3(6) + 1(2λ)) = 0
= -3 + λ -18 + 2λ = 0
= 3λ = 21
= λ = 7