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Question: If \(\overrightarrow{A} = 2\widehat{i} - 3\widehat{j} - \widehat{k}\)and \(\overrightarrow{B} = 4\wi...

If A→=2i^−3j^−k^\overrightarrow{A} = 2\widehat{i} - 3\widehat{j} - \widehat{k}and B→=4i^−6j^−2k^.\overrightarrow{B} = 4\widehat{i} - 6\widehat{j} - 2\widehat{k}. Which of the following is correct?

A

A→andB→\overrightarrow{A}and\overrightarrow{B}are equal vectors

B

A→andB→\overrightarrow{A}and\overrightarrow{B}are perpendicular vectors

C

A→andB→\overrightarrow{A}and\overrightarrow{B}are parallel vectors

D

The dot product of A→andB→\overrightarrow{A}and\overrightarrow{B}is zero

Answer

A→andB→\overrightarrow{A}and\overrightarrow{B}are parallel vectors

Explanation

Solution

Given : A→=2i^−3j^−k^\overset{\rightarrow}{A} = 2\widehat{i} - 3\widehat{j} - \widehat{k}

B→=4i^−6j^−2k^\overset{\rightarrow}{B} = 4\widehat{i} - 6\widehat{j} - 2\widehat{k}

B→=2A→=2(2i^−3j^−k^)=4i^−6j^−2k^\overset{\rightarrow}{B} = 2\overset{\rightarrow}{A} = 2(2\widehat{i} - 3\widehat{j} - \widehat{k}) = 4\widehat{i} - 6\widehat{j} - 2\widehat{k}

Hence, A→\overset{\rightarrow}{A}is parallel to B→\overset{\rightarrow}{B}.