Find the area of the following triangle T.The vertices of T are A(0,0,0), B(3,0,1), and C(1,1,0).The area of triangle T is(Simplify your answer. Type an exact answer, using radicals as needed.)

Answered: Find the area of the following triangle…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the area of the following triangle T.
The vertices of T are A(0,0,0), B(3,0,1), and C(1,1,0).
The area of triangle T is
(Simplify your answer. Type an exact answer, using radicals as needed.)

Expert Solution

Step 1

The objective is to find the area of a triangle whose vertices are $A (0, 0, 0), B (3, 0, 1) a n d C (1, 1, 0)$

Now,

$\begin{array}{rcl} \vec{A B} & = & (3 - 0) i + (0 - 0) j + (1 - 0) k \\ = & 3 i + k \\ \vec{AC} & = & (1 - 0) i + (1 - 0) j + (0 - 0) k \\ = & i + j \end{array}$

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