{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

assig3 - a =[1,1 and b =[1-1(a(3 marks Write[5,1 as a...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 152, Spring 2010 Assignment #3 Notes: Each question is worth 5 marks. Due in class: Monday, January 25 for MWF sections; Tuesday, January 26 for TTh sections. Solutions will be posted Tuesday, January 26 in the afternoon. No late assignments will be accepted. 1. Consider the vectors a = [1, 1, 3] and b = [2,3,-2]. (a) (2 marks) What is the angle between a and b ? Remember that it is better to use the dot product to determine angles between two vectors. (b) (3 marks) What is the area of the parallelogram with a and b as sides? 2. Consider the vectors a = [1, 0, 4], b = [2,-1, 0] and c = [8,-3, 8] (a) (2 marks) Form a matrix A with row vectors a , b and c . Find the determinant of A by hand. (b) (2 marks) What MATLAB commands would you use to check your calculations above? Write out the commands by hand: it is not important to get MATLAB syntax exactly right. Note that there are descriptions of MATLAB commands in your online notes. (c) (1 mark) Based on your answer to part (a), determine whether these vectors lie on a plane. Justify briefly. 3. Consider the vectors
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a = [1,1] and b = [1,-1]. (a) (3 marks) Write [5,1] as a linear combination of a and b , that is find constants c 1 and c 2 such that [5 , 1] = c 1 a + c 2 b (b) (2 marks) Can any vector x with two components be expressed as a linear combination of a and b ? Justify briefly. 4. Let a = [2, 2, 2] and b = [3, 0, 1]. Find all vectors c such that the vectors a , b , c are linearly dependent (that is they all lie on the same plane). 5. Consider the two lines below, given in paramtetric form L 1 : x = (0 , 1 , 2) + s (1 , , 2) L 2 : x = (4 , 2 , c ) + t (-2 , , d ) where c and d are constants. (a) (1 mark) For what value of d are the lines parallel (in the same direction)? (b) (1 mark) With the value of d above, for what value(s) of c (if any) are the two lines identical? Justify briefly. (c) (3 marks) For the case c = 5 and d = 0 find the point P on L 1 and Q on L 2 such that the distance between P and Q is as small as possible....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern