a2 solu - MATH 251-3 Fall 2007 Simon Fraser University...

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Unformatted text preview: MATH 251-3, Fall 2007 Simon Fraser University Assignment 2: Solutions Additional Question Due: 4:30pm, Monday 24 September 2007 1. Consider the four given points A (4 ,- 2 , 3), B (5 , ,- 1), C (4 ,- 3 , 2) and D (2 ,- 7 , 10). (a) Find an equation for the line through the points A and B . Solution: [Note: These solutions give many details of the steps of the calculations; you do not need to show all of these steps.] A direction vector for the line is u =-→ AB =-→ OB--→ OA = h 1 , 2 ,- 4 i ; and the point A (4 ,- 2 , 3) , with position vector r =-→ OA = h 4 ,- 2 , 3 i is a point on the line. Hence the vector equation of the line is (where r = h x,y,z i is the position vector of an arbitrary point on the line) r = r + t u = h 4 ,- 2 , 3 i + t h 1 , 2 ,- 4 i = h 4 + t,- 2 + 2 t, 3- 4 t i , where t ∈ R is a parameter. Alternative forms: The parametric equations for the line are thus x = 4 + t, y =- 2 + 2 t, z = 3- 4 t, and the symmetric equations (non-parametric) are (solving for...
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This note was uploaded on 10/09/2009 for the course MATH macm 101 taught by Professor Jcliu during the Spring '09 term at Simon Fraser.

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a2 solu - MATH 251-3 Fall 2007 Simon Fraser University...

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