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IgorC [24]
3 years ago
13

Given any triangle in the plane, associate to each side an outward pointing normal vector of the same length as the side. Show t

hat the sum of these three vectors is always 0.
Mathematics
1 answer:
Zigmanuir [339]3 years ago
8 0

Let , a, b and c be the length of three sides of triangle, represented in terms of vectors as \vec{a},\vec{b},\vec{c}.

Now, vector of same Magnitude acts as normal vector to each side.

So, equation of any vector p having normal q is given by

      \vec{p} \times\vec{q}

Now sum of three vector and it's normal is given as

    =\vec{a} \times\vec{a}+\vec{b} \times\vec{b}+\vec{c} \times\vec{c}\\\\=0+0+0\\\\=0

Cross product of two identical vectors is Zero.

\rightarrow \vec{i} \times\vec{i}=0

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