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Question 45

Mathematics Scalar and Vector Products Hard

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

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Correct Solution: Option B

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