Kinematics Question 286
Question: The position vectors of points A, B, C and D are $ A=3\hat{i}+4\hat{j}+5\hat{k},B=4\hat{i}+5\hat{j}+6\hat{k},C=7\hat{i}+9\hat{j}+3\hat{k} $ and $ D=4\hat{i}+6\hat{j} $ then the displacement vectors AB and CD are
Options:
A) Perpendicular
B) Parallel
C) Antiparallel
D) Inclined at an angle of $ 60{}^\circ $
Correct Answer: D $ \overrightarrow{AB}=(4\hat{i}+5\hat{j}+6\hat{k})-(3\hat{i}+4\hat{j}+5\hat{k}) $ = $ \hat{i}+\hat{j}+\hat{k} $ $ \overrightarrow{CD}=(4\hat{i}+6\hat{j})-(7\hat{i}+9\hat{j}+3\hat{k}) $ $ =-3\hat{i}-3\hat{j}-3\hat{k} $ $ \overrightarrow{AB} $ and $ \overrightarrow{CD} $ are parallel, because it’s cross-products it’s 0.
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