The points ,

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The points

A

B

C

and

D

have position vectors.

\mathbf{a} = 3\mathbf{i} - 2\mathbf{k}

\mathbf{b} = 5\mathbf{i} - 4\mathbf{j} + \mathbf{k}

\mathbf{c} = 6\mathbf{i} - 3\mathbf{j} + 3\mathbf{k}

and

\mathbf{d} = 4\mathbf{i} + \mathbf{j} + \mathbf{k}

. Determine whether

ABCD

is a parallelogram.