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  • If  <img alt="\mathrm{\overrightarrow{A}=(2 \hat{i}+3 \hat{j}-\hat{k}) \mathrm{m}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Coverrightarrow%7BA%7D%3D%282%20%5Ch

If  \mathrm{\overrightarrow{A}=(2 \hat{i}+3 \hat{j}-\hat{k}) \mathrm{m}} and \mathrm{\overrightarrow{B}=(\hat{i}+2 \hat{j}+2 \hat{k}) \mathrm{m}}.  The magnitude of component of vector \mathrm{\overrightarrow{A}} along vector \mathrm{\overrightarrow{B}} will be ___________ \mathrm{m}.

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

The magnitude of component of vector \mathrm{\bar{A}} along vector \mathrm{\bar{B}} will be

\mathrm{A\cos \Theta =\frac{\mid \bar{A}.\bar{B}\mid }{\mid \bar{B}\mid }}

\mathrm{\bar{A} =2 \hat{i}+3 \hat{\jmath}-\hat{k} }

\mathrm{\bar{B} =\hat{i}+2 \hat{\jmath}+2 \hat{k} }

\mathrm{\bar{A} \cdot \bar{B} =2+6-2=6 }

\mathrm{|\bar{B}| =\sqrt{1^2+2^2+2^2} }

\mathrm{=3 }

\mathrm{A \cos \theta =\frac{\bar{A} \cdot \bar{B}}{|\bar{B}|} }

\mathrm{=\frac{6}{3}=2}

Posted by

Ramraj Saini

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