In Exercises 3 and 4, display the following vectors using arrows on an xy -graph: u , v , − v , −2 v , u + v . u − v , and u − 2 v . Notice that u − v is the vertex of a parallelogram whose other vertices are u , 0 , and − v . 3. u and v as in Exercise 1 4. u and v as in Exercise 2 In Exercises 1 and 2, compute u + v and u − 2 v . 1. u = [ − 1 2 ] , v = [ − 3 − 1 ]
In Exercises 3 and 4, display the following vectors using arrows on an xy -graph: u , v , − v , −2 v , u + v . u − v , and u − 2 v . Notice that u − v is the vertex of a parallelogram whose other vertices are u , 0 , and − v . 3. u and v as in Exercise 1 4. u and v as in Exercise 2 In Exercises 1 and 2, compute u + v and u − 2 v . 1. u = [ − 1 2 ] , v = [ − 3 − 1 ]
In Exercises 3 and 4, display the following vectors using arrows on an xy-graph: u, v, −v, −2v, u + v. u − v, and u − 2v. Notice that u − v is the vertex of a parallelogram whose other vertices are u, 0, and −v.
3. u and v as in Exercise 1 4. u and v as in Exercise 2
In Exercises 1 and 2, compute u + v and u − 2v.
1.
u
=
[
−
1
2
]
,
v
=
[
−
3
−
1
]
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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