Components, displacement and scalar multiples.
Example 1
For u=(7,3) and v=(2,−7), find 2u+v.
The vectors keep their given lengths and directions. Both axes use the same scale.Show worked answer
Answer: (16,−1)
- Multiply both components of u by 2, then add the corresponding components of v.
- 2u+v=(16,−1).
Example 2
A=(5,2) and B=(10,−3). Find vector AB.
Compare the two given positions. Component guides show the route from A to B.Show worked answer
Answer: (5,−5)
- Displacement AB=B−A, component by component.
- AB=(5,−5).
Example 3
For u=(5,8) and v=(7,−5), find 2u+v.
The vectors keep their given lengths and directions. Both axes use the same scale.Show worked answer
Answer: (17,11)
- Multiply both components of u by 2, then add the corresponding components of v.
- 2u+v=(17,11).