Question

The position vectors f three consecutive vertices of a parallelogram are i + j + k, i + 3j + 5k and 7i + 9j + 11k Find the position vector of the fourth vertex.

Answer 1

Let ABCD be a parallelogram.

Let \(\overline{a},\) \(\overline{b},\) \(\overline{c},\) \(\overline{d},\) be the position vectors of the vertices

A, B, C, D of the parallelogram,

Hence, the position vector of the fourth vertex is \(7(\hat{i} + \hat{j} + \hat{k}).\)