Vector Algebra

Topics in this chapter

• Vector Foundations and Operations
• Position Vectors and Section Formula
• Dot Product, Angles and Projection
• Cross Product and Geometric Areas
• Triple Products and Volume
• Direction Vectors and Cosines

Cheat sheet

Practice questions

1. Question 1Q-3A7357

   The vector projection of $\vec a=\hat i+2\hat j+2\hat k$ on $\vec b=2\hat i-\hat j+2\hat k$ is:

   1. A.$\frac{4}{3}(2\hat i-\hat j+2\hat k)$
   2. B.$\frac{4}{9}(2\hat i-\hat j+2\hat k)$
   3. C.$\frac{3}{4}(2\hat i-\hat j+2\hat k)$
   4. D.$\frac{1}{3}(2\hat i-\hat j+2\hat k)$
   See the answer and solution
2. Question 2Q-7B77E7

   For which value of $\lambda$ are the vectors $\vec a=\hat i+2\hat j+3\hat k$, $\vec b=2\hat i-\hat j+\hat k$, and $\vec c=3\hat i+\lambda\hat j+4\hat k$ coplanar?

   1. A.$-1$
   2. B.$0$
   3. C.$1$
   4. D.$5$
   See the answer and solution
3. Question 3Q-F4282D

   Find a unit vector perpendicular to both $\vec a=\hat i+\hat j+\hat k$ and $\vec b=\hat i-\hat j$.

   See the answer and solution
4. Question 4Q-0DA6A9

   Let u = î + 2ĵ − 2k̂ and v = 2î − ĵ + k̂. What is the magnitude of u + v?

   1. A.√7
   2. B.√11
   3. C.3
   4. D.√13
   See the answer and solution
5. Question 5Q-208861

   Vectors a and b are perpendicular, with |a| = 5 and |b| = 12. Find |2a − b|.

   1. A.13
   2. B.√169
   3. C.2√61
   4. D.√244
   See the answer and solution