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Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to the vector v = = (25,20,15).

Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to the vector v = = (25,20,15).

Advanced Engineering Mathematics
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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1. Prove that the intersection line of the planes P,:2x - y - 2z = 0 and P2:x – 2y + z =0 is parallel to the vector v = (25,20,15). 2. Let u = (2,1,3) and v = (2,1,4) be two vectors find the vectors u+v, u – 2v and the unite vector has the same direction of u + v. 3. a) Find the length and direction of the vector A = V3i j. b) Let A and B be two vectors in space, prove that: If A 1 B then A B = 0. 1 Add file
Transcribed Image Text:1. Prove that the intersection line of the planes P,:2x - y - 2z = 0 and P2:x – 2y + z =0 is parallel to the vector v = (25,20,15). 2. Let u = (2,1,3) and v = (2,1,4) be two vectors find the vectors u+v, u – 2v and the unite vector has the same direction of u + v. 3. a) Find the length and direction of the vector A = V3i j. b) Let A and B be two vectors in space, prove that: If A 1 B then A B = 0. 1 Add file
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