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Question Number 132904 by bramlexs22 last updated on 17/Feb/21

$$\mathrm{Find}\mathrm{the}\mathrm{angle}\mathrm{between}\mathrm{the}\mathrm{line}$$$$\frac{\mathrm{x}-2}{3}=\frac{\mathrm{y}+1}{-1}=\frac{\mathrm{z}-3}{2}\mathrm{and}\mathrm{the}$$$$\mathrm{plane}3\mathrm{x}+4\mathrm{y}+\mathrm{z}+5=0$$

Answered by mr W last updated on 17/Feb/21

$$l:(3,-1,2)$$$$n:(3,4,1)$$$$\varphi =90°-\theta$$$$=90°-{\cos }^{-1}\frac{l\cdot n}{\mid l\mid \mid n\mid }$$$$={\sin }^{-1}\frac{l\cdot n}{\mid l\mid \mid n\mid }$$$$={\sin }^{-1}\frac{(9-4+2)}{\sqrt{(9+1+4)(9+16+1)}}$$$$=21.525°$$

Commented by liberty last updated on 17/Feb/21

$$\mathrm{why}\mathrm{n}:(3,4,5)?\mathrm{it}\mathrm{should}(3,4,1)$$

Commented by mr W last updated on 17/Feb/21

$${it}^{\prime }smisread.thanksforpointingout!$$

Commented by mr W last updated on 17/Feb/21

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