Let $\rm \vec{a}$, $\rm \vec{b}$ and $\rm \vec{c}$ be the position vectors of the three vertices A, B, C of a triangle respectively. Then the area of this triangle is given by:

Question

Let $\rm \vec{a}$, $\rm \vec{b}$ and $\rm \vec{c}$ be the position vectors of the three vertices A, B, C of a triangle respectively. Then the area of this triangle is given by:

TuteeHUB · Accepted Answer

$\rm \vec{a}\times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}$

TuteeHUB · Answer

$\rm \dfrac{1}{2} (\vec{a}\times \vec{b})\vec{c}$

TuteeHUB · Answer

$\rm \dfrac{1}{2} |\vec{a}\times \vec{b} + \vec{b} \times \vec{c}+\vec{c}\times \vec{a}|$

TuteeHUB · Answer

None of these

1.	Let \(\rm \vec{a}\), \(\rm \vec{b}\) and \(\rm \vec{c}\) be the position vectors of the three vertices A, B, C of a triangle respectively. Then the area of this triangle is given by:
A.	\(\rm \dfrac{1}{2} (\vec{a}\times \vec{b})\vec{c}\)
B.	\(\rm \dfrac{1}{2} \|\vec{a}\times \vec{b} + \vec{b} \times \vec{c}+\vec{c}\times \vec{a}\|\)
C.	\(\rm \vec{a}\times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}\)
D.	None of these
Answer» C. \(\rm \vec{a}\times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}\)

Let \(\rm \vec{a}\), \(\rm \vec{b}\) and \(\rm \vec{c}\) be the position vectors of the three vertices A, B, C of a triangle respectively. Then the area of this triangle is given by:

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