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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.) %3D The area is (Type an exact answer, using radicals as needed.)

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.) %3D The area is (Type an exact answer, using radicals as needed.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.)
Transcribed Image Text: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 and u-v=2-16,2-0,2-16 =-14,2,-14

Let, u-v=w=-14,2,-14

Then uv=16-2,0-2,16-2=14,-2,14 and uw=-14-2,2-2,-14-2=-16,0,-16

Now,

uv×uw=ijk14-214-160-16=32-0i-0j+0-32k=32i-32k 

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