The points , and are three vertices of a parallelogram ,…

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

The points

A(4, 5, 10)

B(2, 3, 4)

and

C(1, 2, -1)

are three vertices of a parallelogram

ABCD

, then (1) Vector equation of

AB

2\mathbf{i} + 3\mathbf{j} + 4\mathbf{k} + \lambda(\mathbf{i} + \mathbf{j} + 3\mathbf{k})

(2) Cartesian equation of

BC

\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{5}

(3) Coordinates of

D

are

(3, 4, 5)

(4)

ABCD

is a rectangle