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  • The unit vector parallel to the resultant of the vectors <img alt="\vec{A}=4\hat{i}+3\hat{j}+6\hat{k}\And \vec{B}=-\hat{i}+3\hat{j}-8\hat{k}" src="https://entrancecorner.oncodecogs.com/gif.lat

The unit vector parallel to the resultant of the vectors \vec{A}=4\hat{i}+3\hat{j}+6\hat{k}\And \vec{B}=-\hat{i}+3\hat{j}-8\hat{k} is, 

Option: 1

\frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k})


Option: 2

\frac{1}{7}(3 \hat{i}+6 \hat{j}+2 \hat{k})


Option: 3

\frac{1}{49}(3 \hat{i}+6 \hat{j}+2 \hat{k})


Option: 4

\frac{1}{49}(3 \hat{i}+6 \hat{j}-2 \hat{k})


Answers (1)

best_answer

The resultant of  \vec{A}\: \And \: \vec{B} is given by,

\\\vec{R}=\vec{A}+\vec{B} \\ \\\vec{R}=(4\hat{i}+3\hat{j}+6\hat{k})+(-\hat{i}+3\hat{j}-8\hat{k}) \\ \\\vec{R}=(3\hat{i}+6\hat{j}-2\hat{k}) \\

Hence, unit vector in direction of {\vec{R}} is given as

\\\hat{R}=\frac{{\vec{R}}}{\left| {\vec{R}} \right|} \\

\\\hat{R}=\frac{3\hat{i}+6\hat{j}-2\hat{k}}{7} \\

Posted by

Ritika Jonwal

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