Find the area of the triangle T with sides u= (2,2,2), v = (16,0,16), and u - v. (The area of a triangle is half the area of the corresponding parallelogram.)The area is(Type an exact answer, using radicals as needed.)

Answered: Find the area of the triangle T with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Find the area of the triangle T with sides u= (2,2,2), v = (16,0,16), and u - v. (The area of a triangle is half the area of the corresponding parallelogram.)
The area is
(Type an exact answer, using radicals as needed.)

Expert Solution

Step 1

The objective is to find the area of the triangle T with sides

$u = <2, 2, 2>, v = <16, 0, 16> a n d u - v = <2 - 16, 2 - 0, 2 - 16> = <- 14, 2, - 14>$

Let, $u - v = w = <- 14, 2, - 14>$

Then $u v = <16 - 2, 0 - 2, 16 - 2> = <14, - 2, 14> a n d u w = <- 14 - 2, 2 - 2, - 14 - 2> = <- 16, 0, - 16>$

Now,

$\begin{array}{rcl} u v \times u w & = & |\begin{matrix} i & j & k \\ 14 & - 2 & 14 \\ - 16 & 0 & - 16 \end{matrix}| \\ = & (32 - 0) i - (0) j + (0 - 32) k \\ = & 32 i - 32 k \end{array}$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions