The value of lambda for which the four points A(3, 2, 1), B(4, lambda, 5), C(4, 2, -2), D(6, 5, -1) are coplanar is:

The position vector of a point R dividing PQ externally in ratio 2:1, where P and Q have position vectors 2**i** + **j** and **i** + 3**j**, is:

The vector **a** = 2**i** - **j** + **k**, **b** = **i** + 2**j** - 3**k**, **c** = 3**i** + lambda**j** + 5**k** are coplanar when lambda equals:

A vector of magnitude 6 perpendicular to both **i** + **j** + **k** and **i** - 2**j** + **k** is:

The position vectors of vertices of a triangle are **i** + 3**j**, 3**i** - **j**, and -**i** + **j**. Its area is: