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Q. 10

Expert-verified
Found in: Page 823

### Calculus

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 ${\mathrm{ℝ}}^{3}$? How do you find the area of this triangle?

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

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

See the step by step solution

## Step 1. Given Information

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

## Step 2. Firstly explaining meant by the triangle determined by vectors u and v in ℝ3

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.

## Step 3. We can express the area of a triangle by vectors also.

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