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  • Let <img alt="\vec{a}=2\hat{i}-3\hat{j}+6\hat{k},\, \vec{b}=\hat{i}+\hat{j}-\hat{k},\,\vec{c}=-\hat{i}+4\hat{j}-7\hat{k},\, \vec{d}=\hat{i}-4\hat{j}+7\hat{k}" src="https://learn.careers360.com/late

Let \vec{a}=2\hat{i}-3\hat{j}+6\hat{k},\, \vec{b}=\hat{i}+\hat{j}-\hat{k},\,\vec{c}=-\hat{i}+4\hat{j}-7\hat{k},\, \vec{d}=\hat{i}-4\hat{j}+7\hat{k} then which of the following represents two equal vectors

Option: 1

\vec{a}+\vec{b}, \vec{c}+\vec{d}


Option: 2

\vec{a}+\vec{c}, \vec{b}


Option: 3

\vec{b}+\vec{c}, \vec{a}


Option: 4

None of these


Answers (1)

best_answer

As we learned

Equal Vectors -

Two vectors are said to be equal if they have the same magnitude, direction and represent the same physical quantity.

- wherein

\vec{a}= \vec{b} if \mid \vec{a}\mid = \mid \vec{b}\mid and direction of \vec{a} , \vec{b} are same.

 

 \vec{a}+\vec{b}=3\hat{i}-2\hat{j}+5\hat{k}

\vec{c}+\vec{d}=\vec{0}

\vec{a}+\vec{c}=\hat{i}+\hat{j}-\hat{k}

\vec{b}+\vec{c}=0\hat{i}+5\hat{j}-8\hat{k}

We can see, Option (B) gives equal vectors both being equal to \hat{i}+\hat{j}-\hat{k}

\therefore Option (B)

 

Posted by

avinash.dongre

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