Math Analysis Honors – Worksheet 104
Vector Arithmetic
In Exercises 1-3, find u  v . Draw a diagram to represent “tail-to-head” addition of the two vectors. Find the magnitude
of the resultant vector.
2
19
1) u  2,4 , v  6,1
2) u  4,0 , v  1, 3
3) u  , 4 , v  7,
3
3
In Exercises 4-11, let u  1,3 , v  2,4 , and w  2, 5 . Find the component form and magnitude of each resultant
vector.
4) u + v
6) u  w
7) 3v
5) u   1 v
8) 2u  3w
9) 2u  4v
10) 2u  3v
11) u  v
In Exercises 12-15, find a unit vector in the direction of the given vector. Verify that the magnitude of the unit vector is 1.
14) w  i  2 j
15) w  5i  5j
12) u  2,4
13) v  1, 1
In Exercises 16-19, find the unit vector in the direction of the given vector. Write your answer in (a) component form and
(b) as a linear combination of the standard unit vectors i and j.
16) u  2,1
17) u  3,2
18) u  4, 5
19) u  3, 4
Math Analysis Honors – Worksheet 104
Vector Arithmetic
In Exercises 1-3, find u  v . Draw a diagram to represent “tail-to-head” addition of the two vectors. Find the magnitude
of the resultant vector.
2
19
1) u  2,4 , v  6,1
2) u  4,0 , v  1, 3
3) u  , 4 , v  7,
3
3
In Exercises 4-11, let u  1,3 , v  2,4 , and w  2, 5 . Find the component form and magnitude of each resultant
vector.
4) u + v
6) u  w
7) 3v
5) u   1 v
8) 2u  3w
9) 2u  4v
10) 2u  3v
11) u  v
In Exercises 12-15, find a unit vector in the direction of the given vector. Verify that the magnitude of the unit vector is 1.
14) w  i  2 j
15) w  5i  5j
12) u  2,4
13) v  1, 1
In Exercises 16-19, find the unit vector in the direction of the given vector. Write your answer in (a) component form and
(b) as a linear combination of the standard unit vectors i and j.
16) u  2,1
17) u  3,2
18) u  4, 5
19) u  3, 4