DEPARTMENT
MTH405_Wk_7_Tutorial

# MTH405_Wk_7_Tutorial - MTH405 Wk 7 Tutorial 1 Sketch the...

• Homework Help
• 2

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MTH405 Wk 7 Tutorial 1. Sketch the vectors with their initial points at the origin. b.) − 5ˆi + 3ˆj d.) 3ˆi − 2ˆj a.) h2, 5i c.) h−5, −4i −−−→ 2. Find the components of the vector P1 P2 and sketch them. (Note that −−−→ vectors denoted as P1 P2 have starting point as P1 and terminating point as P2 .) (a) P (3, 5), P (2, 8) (b) P1 (0, 0), P2 (3, 4) (c) P1 (4, 1), P2 (0, 0) 3. Let p~ = 3ˆi − kˆ, ~q = ˆi − ˆj + 2kˆ and ~r = 3ˆj . Find a.) ~r − ~q b.) 6~ p + 4~r c.) − ~q − 2~r d.) 4(3~ p + ~q) e.) − 8(~q + ~r) + 2~ p f.) 3~r − (~q − ~r) 4. For the following vectors, nd its norm and then use it to normalise the vectors. a.) h3, 4i c.) h0, 3, 0i √ √ b.) 2ˆi − 7ˆj d.) ~v = ˆi + ˆj + kˆ 5. Let ~u = ˆi − 3ˆj + 2kˆ, ~v = ˆi + ˆj , and w ~ = 2ˆi + 2ˆj − 4kˆ. Find a.) ||~u|| ~ c.) ||w|| e.) ||3~u + 5~v + w|| ~ 1 g.) w ~ ||w|| ~ b.) ||~v || d.) ||~u + ~v || 1 f.) w ~ ||w|| ~ 1 6. Find the unit vectors that satisfy the stated conditions. (a) Same direction as −ˆi + 4ˆj . (b) Oppositely directed to 6ˆi − 4ˆj + 2kˆ. (c) Same direction as the vector from the point A(−1, 0, 2) to the point B(3, 1, 1). 7. In each part, nd the dot product of the vectors and the angle between them. (a) ~u = ˆi + 2ˆj , ~v = 6ˆi − 8ˆj . (b) ~u = h−7, −3i, ~v = h0, 1i. (c) ~u = ˆi − 3ˆj + 7kˆ, ~v = 8ˆi − 2ˆj − 2kˆ. (d) ~u = h−3, 1, 2i, ~v = h4, 2, −5i. 8. In each part, use the information given to nd ~u · ~v . (a) ||~u|| = 1, ||~v || = 2, the angle between ~u and ~v is π6 . (b) ||~u|| = 2, k|~v || = 3, the angle between ~u and ~v is 135◦ . 9. In each part, nd the vector component of ~v along ~b and the vector component of ~v orthogonal to ~b. Then sketch the vectors ~v , projb~v and ~v − projb~v . (a) ~v = 2ˆi − ˆj , ~b = 3ˆi + 4ˆj . (b) ~v = h4, 5i, ~b = h1, 2i. (c) ~v = −3ˆi − 2ˆj , ~b = 2ˆi + ˆj . 10. Show that the three vectors ~v1 ~v2 ~v3 3ˆi − ˆj + 2kˆ = ˆi + ˆj − kˆ = ˆi − 5ˆj − 4kˆ = are pairwise orthogonal. 2 ...
View Full Document

• Spring '16
• Alveen Chand
• Dot Product, Vector Motors, ~v

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern