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  • If ,<img alt="\vec{A}=3\hat{i}+4\hat{j}\And \vec{B}=7\hat{i}+24\hat{j}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cvec%7BA%7D%3D3%5Chat%7Bi%7D&plus;4%5Chat%7Bj%7D%5CAnd%2

If ,\vec{A}=3\hat{i}+4\hat{j}\And \vec{B}=7\hat{i}+24\hat{j}the vector having the same magnitude as B and parallel to A is,

Option: 1

5\hat{i}+20\hat{j}


Option: 2

15\hat{i}+10\hat{j}


Option: 3

20\hat{i}+15\hat{j}


Option: 4

15\hat{i}+20\hat{j}


Answers (1)

best_answer

\vec{A}=3\hat{i}+4\hat{j} \\ \left| {\vec{A}} \right|=\sqrt{{{3}^{2}}+{{4}^{2}}}=5 \\ \vec{B}=7\hat{i}+24\hat{j} \\ \left| {\vec{B}} \right|=\sqrt{{{7}^{2}}+{{24}^{2}}}=25 \\

Let the vector having same magnitude of B and parallel to A vector be \vec{C}

\left| {\vec{C}} \right|=25

Thus,

\vec{C}=\left| {\vec{C}} \right|\hat{C}

Where, \hat{C}=\hat{A}

\hat{A}=\frac{{\vec{A}}}{\left| {\vec{A}} \right|}=\frac{3\hat{i}+4\hat{j}}{5} \\ \vec{C}=\left| {\vec{C}} \right|\hat{C} \\ \vec{C}=25\times \frac{3\hat{i}+4\hat{j}}{5} \\ \vec{C}=5(3\hat{i}+4\hat{j}) \\ \vec{C}=15\hat{i}+20\hat{j} \\

 

Posted by

SANGALDEEP SINGH

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