Find angle between vec A = 3hat i - hat | vedclass

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Question

$\cos 	heta=\frac{\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}}{\mathrm{AB}}=\frac{(3 \hat{\mathrm{i}}-\hat{j}+4 \hat{\mathrm{k}}) \

Vedclass · Accepted Answer

${	an ^{ - 1}}\,\left( {\frac{{\sqrt {10} }}{4}} ight)$

Vedclass · Answer

$\cos 	heta=\frac{\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}}{\mathrm{AB}}=\frac{(3 \hat{\mathrm{i}}-\hat{j}+4 \hat{\mathrm{k}}) \cdot(\hat{\mathrm{k}})}{\sqrt{(3)^{2}+(-1)^{2}+(4)^{2}} \sqrt{(1)^{2}}}=\frac{4}{\sqrt{26}}$

Base $=4,$ hypotenuse $=\sqrt{26} \cdot$ perpendicular $=\sqrt{10}$

$	an 	heta=\frac{\sqrt{10}}{4}, \quad 	heta=	an ^{-1}\left(\frac{\sqrt{10}}{4}ight)$

Find angle between $\vec A = 3\hat i - \hat j + 4\hat k$ and $Z-$ axis

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