Question

The figure formed by the four points $\mathbf{i} + \mathbf{j} - \mathbf{k},2\mathbf{i} + 3\mathbf{j},$ $3\mathbf{i} + 5\mathbf{j} - 2\mathbf{k}$ and $\mathbf{k} - \mathbf{j}$ is

• A. Rectangle
• B. Parallelogram
• C. Trapezium
• D. None of these

Answer 1

Answer: (C)

Trapezium

Answer 2

Let $A \equiv (1,1, - 1),B \equiv (2,3,0),C \equiv (3,5, - 2),D \equiv (0, - 1,1)$

So, $\overset{\rightarrow}{AB} = (1,2,1),\overset{\rightarrow}{BC} = (1,2, - 2),\overset{\rightarrow}{CD} = ( - 3, - 6,3),\overset{\rightarrow}{DA} = (1,2, - 2)$

Clearly, $\overset{\rightarrow}{BC}||\overset{\rightarrow}{DA},$ but $AB \neq CD$So, it is a trapezium.