7.1. Basic Properties of Vectors http://www.ck12.org
3.A= ( 1 , 3 ),−→v=< 4 , 8 >,−→u =<− 1 ,− 5 > .A+−→v+−→u = ( 4 , 6 ).
Practice
- Describe what a vector is and give a real-life example of something that a vector could model.
Consider the points:A( 3 , 5 ),B(− 2 ,− 4 ),C( 1 ,− 12 ),D(− 5 , 7 ). Find the vectors in component form of:
2.−→AB
3.−→BA
4.−→AC
5.CB−→
6.−→AD
7.−→DA - What isC+−→CB? Compute this algebraically and describe why the answer makes sense.
- Use your answer to the previous problem to help you determineD+−→DAwithout doing any algebra.
- A ship is traveling SSW at 13 knots. Describe this ship’s movement in a vector.
- A vector that describes a ships movement is< 5
√
2 , 5
√
2 >. What direction is the ship traveling in and what is
its speed in knots?
For each of the following vectors, draw the vector on a coordinate plane starting at the origin and find its magnitude.
12.< 3 , 7 >
13.<− 3 , 4 >