In triangle ABC,if alpha, beta and gamma are | vedclass

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Question

(D) Let $ABC$ be a triangle with position vectors $\alpha, \beta, \gamma$ for vertices $A, B, C$ respectively. Let $AM$ be the perpendicular from $A$

Vedclass · Accepted Answer

$\frac{|\alpha 	imes \beta + \beta 	imes \gamma + \gamma 	imes \alpha|}{|\gamma - \beta|}$

Vedclass · Answer

(D) Let $ABC$ be a triangle with position vectors $\alpha, \beta, \gamma$ for vertices $A, B, C$ respectively. Let $AM$ be the perpendicular from $A$ to $BC$.The area of $	riangle ABC$ is given by:$	ext{Area} = \frac{1}{2} |BC| \cdot |AM|$Also,the area of $	riangle ABC$ in terms of position vectors is:$	ext{Area} = \frac{1}{2} |\alpha 	imes \beta + \beta 	imes \gamma + \gamma 	imes \alpha|$Equating the two expressions for the area:$\frac{1}{2} |BC| \cdot |AM| = \frac{1}{2} |\alpha 	imes \beta + \beta 	imes \gamma + \gamma 	imes \alpha|$Since the length of the side $BC$ is $|\gamma - \beta|$,we have:$|\gamma - \beta| \cdot |AM| = |\alpha 	imes \beta + \beta 	imes \gamma + \gamma 	imes \alpha|$Therefore,the length of the perpendicular $AM$ is:$|AM| = \frac{|\alpha 	imes \beta + \beta 	imes \gamma + \gamma 	imes \alpha|}{|\gamma - \beta|}$

In $\triangle ABC$,if $\alpha, \beta$ and $\gamma$ are the position vectors of the vertices $A, B$ and $C$ respectively,then the length of the perpendicular from $A$ to $BC$ is

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