The area of a triangle formed by the tips of vectors a, b and c is

1/2 (a − b)·(a − c)
1/2 |(a − b)×(a − c)|
1/2 |a×b×c|
1/2 (a×b)·c

Correct answer: 1/2 |(a − b)×(a − c)|

Solution

The area of a triangle formed by two vectors can be calculated using the cross product, which gives the magnitude of the parallelogram spanned by the vectors. Dividing by two yields the area of the triangle, hence the correct option is 1/2 |(a − b)×(a − c)|.

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