solutions5_2011

solutions5_2011 - Math 152, Spring 2011 Solutions...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 152, Spring 2011 Solutions Assignment #5 Notes: Each question is worth 5 marks. Due in class: Monday, February 7 for MWF sections; Tuesday, Febru- ary 8 for TTh sections. Solutions will be posted Tuesday, February 8 in the afternoon. No late assignments will be accepted. (1) (a) (1 mark) Find the equation form of the plane P with normal vector b = [1 , ,- 1] and passing through the point q = [0 ,- 1 , 0]. (b) (1 mark) Find the equation form of the line L that is perpendicular to the plane Q with equation- x +3 y +2 z = 1 and passing through the origin. (c) (3 marks) Use Gaussian elimination to determine the intersection between the plane P and the the line L . Solution: (a) The equation form of the plane P is x 1 + 0 x 2- x 3 = b q = 0; that is x 1- x 3 = 0 . (b) Since the equation form of the plane Q is the equation- x 1 + 3 x 2 + 2 x 3 = 1 , then a normal vector to the plane Q is the vector b 1 = [- 1 , 3 , 2]. This vector is in turn parallel to the line L . Since the line L passes through the origin its parametric equations are x = t b 1 = t [- 1 , 3 , 2]; that is, x 1 =- t, x 2 = 3 t, x 3 = 2 t. We can use these to find the equation form of the line L . In this case we obtain 3 x 1 + x 2 = 0 2 x 1 + x 3 = 0 . (c). The intersection of the plane P and the line L is the solution of the system of equation x 1- x 3 = 0 3 x 1 + x 2 = 0 2 x 1 + x 3 = 0 . The augmented matrix associated to this system is 1 2 1 0- 1 | 3 1 | 2 0 1 | Applying Gaussian elimination we obtain the echelon form 1 0- 1 | 0 1 3 | 0 0 3 | We can use this system using backwards substitution. In this case we get x 1 = x 2 = x 3 = 0. Thus the intersection between P and L is the point [0 , , 0]. (2) (a) (2 marks) Use Gaussian elimination to find the set of solutions to the following homogeneous system. Present your answer in parametric form....
View Full Document

Page1 / 7

solutions5_2011 - Math 152, Spring 2011 Solutions...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online