1 Vectors 2 Systems Of Linear Equations 3 Matrices 4 Eigenvalues And Eigenvectors 5 Orthogonality 6 Vector Spaces 7 Distance And Approximation Chapter1: Vectors
1.1 The Geometry And Algebra Of Vectors 1.2 Length And Angle: The Dot Product 1.3 Lines And Planes 1.4 Applications Chapter Questions Section1.2: Length And Angle: The Dot Product
Problem 1EQ: In Exercises 1-6, find .
1.
Problem 2EQ: In Exercises 1-6, find .
2.
Problem 3EQ: In Exercises 1-6, find uv. u=[123],v=[231] Problem 4EQ: In Exercises 1-6, find uv. u=[3.20.61.4],v=[1.54.10.2] Problem 5EQ: In Exercises 13-16, find the distance d(u,v)between u and v in the given exercise. Exercise 3 Problem 6EQ: In Exercises 1-6, find .
6.
Problem 7EQ: In Exercises 7-12, find for the given exercise, and give a unit vector in direction of .
7.... Problem 8EQ: In Exercises 7-12, find u for the given exercise, and give a unit vector in direction of u. Exercise... Problem 9EQ: In Exercises 7-12, find for the given exercise, and give a unit vector in direction of .
9.... Problem 10EQ: In Exercises 7-12, find u for the given exercise, and give a unit vector in direction of u. Exercise... Problem 11EQ: In Exercises 7-12, find for the given exercise, and give a unit vector in direction of .
11.... Problem 12EQ: In Exercises 7-12, find u for the given exercise, and give a unit vector in direction of u. Exercise... Problem 13EQ: In Exercises 13-16, find the distance between and in the given exercise.
13. Exercise 1
Problem 14EQ: In Exercises 13-16, find the distance between and in the given exercise.
14. Exercise 2
Problem 15EQ Problem 16EQ Problem 17EQ Problem 18EQ: In Exercises 18-23, determine whether the angle between and is acute, obtuse, or a right... Problem 19EQ: In Exercises 18-23, determine whether the angle between u and v is acute, obtuse, or a right angle.... Problem 20EQ: In Exercises 18-23, determine whether the angle between and is acute, obtuse, or a right... Problem 21EQ: In Exercises 18-23, determine whether the angle between u and v is acute, obtuse, or a right angle.... Problem 22EQ: In Exercises 18-23, determine whether the angle between u and v is acute, obtuse, or a right angle.... Problem 23EQ Problem 24EQ Problem 25EQ Problem 26EQ Problem 27EQ Problem 28EQ Problem 29EQ Problem 30EQ Problem 31EQ Problem 32EQ Problem 33EQ Problem 34EQ Problem 35EQ Problem 36EQ Problem 37EQ Problem 38EQ Problem 39EQ Problem 40EQ Problem 41EQ Problem 42EQ:
In Exercises 40-45, find the projection of v onto u.
42. u = , v =
Problem 43EQ: In Exercises 40-45, find the projection of vontou. u=[1-11-1],v=[1-11-1] Problem 44EQ Problem 45EQ Problem 46EQ Problem 47EQ Problem 48EQ: In Exercises 48 and 49, find all values of the scalar k for which the two vectors are orthogonal.... Problem 49EQ: In Exercises 48 and 49, find all values of the scalar k for which the two vectors are... Problem 50EQ: Describe all vectors v=[xy] that are orthogonal to u=[31]. Problem 51EQ Problem 52EQ Problem 53EQ Problem 54EQ Problem 55EQ Problem 56EQ Problem 57EQ Problem 58EQ Problem 59EQ Problem 60EQ Problem 61EQ Problem 62EQ Problem 63EQ Problem 64EQ Problem 65EQ Problem 66EQ Problem 67EQ Problem 68EQ Problem 69EQ Problem 70EQ Problem 71EQ Problem 72EQ Problem 73EQ Problem 74EQ Problem 1AEXP Problem 2AEXP Problem 3AEXP Problem 4AEXP Problem 5AEXP Problem 6AEXP Problem 7AEXP Problem 8AEXP Problem 34EQ
Give the vector result of a + b + c as a sum of its i and j components. [Give an answer using the letters i and j, such as 15i+ 29 j.]
Transcribed Image Text: On the grid below, draw the following vectors:
a
-21+ 3j
b = −4+2j
c = 57
8
7
6
5
4
3
2
-8-7-6
-4-3-2-1
-1
-2
-3
-4
-5
-6
-7
-8 +
Clear All Draw:
2
a
8
Part 2 of 2
Give the vector result of a + b + c as a sum of its i and j components. [Give an answer using the letters į and
j, such as 15i 29j.]
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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![On the grid below, draw the following vectors:
a
-21+ 3j
b = −4+2j
c = 57
8
7
6
5
4
3
2
-8-7-6
-4-3-2-1
-1
-2
-3
-4
-5
-6
-7
-8 +
Clear All Draw:
2
a
8
Part 2 of 2
Give the vector result of a + b + c as a sum of its i and j components. [Give an answer using the letters į and
j, such as 15i 29j.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70295faf-d188-48da-8b46-ee8193f4f21a%2F89ff7b8b-2f21-4c64-9aec-a498652fa033%2Ffcnjnnv_processed.jpeg&w=3840&q=75)
