If vectors a, b, and c represent the sides BC | vedclass

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(B) In a triangle $ABC$,the sides are represented by vectors $\vec{BC} = a$,$\vec{CA} = b$,and $\vec{AB} = c$.By the triangle law of vector addition,t

Vedclass · Accepted Answer

$a 	imes b = b 	imes c = c 	imes a$

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(B) In a triangle $ABC$,the sides are represented by vectors $\vec{BC} = a$,$\vec{CA} = b$,and $\vec{AB} = c$.By the triangle law of vector addition,the sum of vectors representing the sides of a triangle taken in order is zero.Thus,$\vec{BC} + \vec{CA} + \vec{AB} = 0$,which implies $a + b + c = 0$.Taking the cross product of this equation with $a$:$a 	imes (a + b + c) = a 	imes 0$$a 	imes a + a 	imes b + a 	imes c = 0$Since $a 	imes a = 0$,we get $a 	imes b = c 	imes a$.Similarly,taking the cross product with $b$:$b 	imes (a + b + c) = b 	imes 0$$b 	imes a + b 	imes b + b 	imes c = 0$$b 	imes a + b 	imes c = 0 \implies a 	imes b = b 	imes c$.Therefore,$a 	imes b = b 	imes c = c 	imes a$.

If vectors $a, b,$ and $c$ represent the sides $BC, CA,$ and $AB$ of a triangle $ABC$ respectively,then which of the following is true?

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