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Q. 10

Expert-verifiedFound in: Page 823

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

What is meant by the triangle determined by vectors *u* and *v* in ${\mathrm{\mathbb{R}}}^{3}$? How do you find the area of this triangle?

Vectors *u* and *v* are visualized as directed line segments whose lengths are their magnitudes.

$\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{determined}\mathrm{by}\mathrm{the}\mathrm{two}\mathrm{vectors}=\frac{1}{2}\left|\overrightarrow{A}\times \overrightarrow{B}\right|$

What is meant by the triangle determined by vectors *u* and *v* in ${\mathrm{\mathbb{R}}}^{3}$? How do you find the area of this triangle?

Vectors *u* and *v* are visualized as directed line segments whose lengths are their magnitudes. We will use this concept well in this concept explanation, the area of a triangle formed by vectors. Normally when we try to find out the area of a triangle, we usually find out the value by the formula of Heron’s Formula.

$\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}\mathrm{determined}\mathrm{by}\mathrm{the}\mathrm{two}\mathrm{vectors}=\frac{1}{2}\left|\overrightarrow{A}\times \overrightarrow{B}\right|$

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