This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: B U Department of Mathematics Math 102 Calculus II Fall 2005 Final This archive is a property of Bo˘gazi¸ ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a nonprofit service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without nonprofit purpose may result in severe civil and criminal penalties. 1. (a) Find an equation for the plane through A (0 , , 1) , B (2 , , 0) , and C (0 , 3 , 0). (b) Find the cosine of the angle between this plane and xyplane. (c) Find the area of the triangle ABC. Solution: (a) We find a vector normal to the plane and use it with one of the points (it doesn’t matter which) to write an equation for the plane.→ AB = < 2 , , 1 > = < 2 , , 1 >→ AC = < , 3 , 1 > = < , 3 , 1 > The cross product→ AB ×→ AC = ~ i ~ j ~ k 2 0 1 0 3 1 = 3 ~ i + 2 ~ j + 6 ~ k is normal to the plane. By using components of this vector and coordinates of the point (0,0,1) we can write the equation of the plane as 3( x 0) + 2( y 0) + 6( z 1) = 0 3 x + 3 y + 6 z = 6 (b) The angle between two intersecting planes is defined to be the (acute) angle determined by their normal vectors....
View
Full
Document
This note was uploaded on 04/30/2008 for the course C CMPE 150 taught by Professor Tuna during the Spring '08 term at Boğaziçi University.
 Spring '08
 Tuna

Click to edit the document details