Question

The position vectors of points A, B, C and D are

$A = 3\widehat{i} + 4\widehat{j} + 5\widehat{k},B = 4\widehat{i} + 5\widehat{j} + 6\widehat{k},C = 7\widehat{i} + 9\widehat{j} + 3\widehat{k}$ and

$D = 4\widehat{i} + 6\widehat{j}$ then the displacement vectors AB and CD are

• A. Perpendicular
• B. Parallel
• C. Antiparallel
• D. Inclined at an angle of 60°

Answer 1

Answer: (D)

Inclined at an angle of 60°

Answer 2

$\overset{\rightarrow}{AB} = (4\widehat{i} + 5\widehat{j} + 6\widehat{k}) - (3\widehat{i} + 4\widehat{j} + 5\widehat{k})$ =$\widehat{i} + \widehat{j} + \widehat{k}$

$\overset{\rightarrow}{CD} = (4\widehat{i} + 6\widehat{j}) - (7\widehat{i} + 9\widehat{j} + 3\widehat{k})$ $= - 3\widehat{i} - 3\widehat{j} - 3\widehat{k}$

$\overset{\rightarrow}{AB}$ and $\overset{\rightarrow}{CD}$ are parallel, because its cross-products is 0.