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(C) The vector area of a triangle with vertices having position vectors $a, b, c$ is given by the formula: $	ext{Vector Area} = \frac{1}{2} \vec{AB}

Vedclass · Accepted Answer

$\frac{1}{2}(a 	imes b + b 	imes c + c 	imes a)$

Vedclass · Answer

(C) The vector area of a triangle with vertices having position vectors $a, b, c$ is given by the formula: $	ext{Vector Area} = \frac{1}{2} \vec{AB} 	imes \vec{AC}$ Since $\vec{AB} = b - a$ and $\vec{AC} = c - a$,we have: $	ext{Vector Area} = \frac{1}{2} (b - a) 	imes (c - a)$ Expanding the cross product: $	ext{Vector Area} = \frac{1}{2} (b 	imes c - b 	imes a - a 	imes c + a 	imes a)$ Since $a 	imes a = 0$ and $-b 	imes a = a 	imes b$,and $-a 	imes c = c 	imes a$: $	ext{Vector Area} = \frac{1}{2} (a 	imes b + b 	imes c + c 	imes a)$ Thus,the correct option is $C$.

Let $a, b, c$ be the position vectors of the vertices of a triangle $ABC$. The vector area of triangle $ABC$ is

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