{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

practice midterm 1

practice midterm 1 - SOLUTIONS TO 18.02 PRACTICE MIDTERM#1...

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

View Full Document Right Arrow Icon
SOLUTIONS TO 18.02 PRACTICE MIDTERM #1 BJORN POONEN October 1, 2009 1) Let A , B , and P be points in space such that P is on the line segment AB and the distance AP is twice the distance BP . Find the position vector P in terms of the position vectors A and B . Solution: Let r ( t ) be the position of a particle moving with constant speed along ←→ AB so that it is at A at t = 0 and at B at t = 1. Then P is the point at time t = 2 / 3 (since 2 / 3 = 2(1 - 2 / 3)). We have r ( t ) = A + t ( B - A ), so r (2 / 3) = 1 3 A + 2 3 B . 2) What is the upper right entry of 6 5 4 3 2 1 0 1 - 2 3 0 - 4 5 - 6 0 T ? Solution: It is the dot product of the first row of the first matrix with the last column of the transposed second matrix. That column is the the last row of the untransposed second matrix. So the answer is 6 , 5 , 4 · 5 , - 6 , 0 = 0 . 3) Let a be a nonzero vector. What is the geometric shape formed by the set of points P in space whose position vector P satisfies | P × a | = 1?
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.

{[ 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