Dot and Triple Product Problems

Solutions

1Given the vectors Vector U, Vector V and Vector W, calculate the following:

1. Vector Problem, Vector Problem

2. Triple Product Problem, Triple Product Problem

3. Vector Problem

4. Vector Magnitude Vector Magnitude

5. Vector Cosine

2For what values of a do the vectors Vector U, Vector V and Vector W form a basis?

3Determining the value of the coefficient k for the vectors Vector X = kVector U − 2Vector V + 3Vector W, Vector Y = −vector u + kVector V + Vector W if the vectors are:

1. Orthogonal.

2. Parallel.

4Find the direction cosines of the vector Vector U.

5Calculate the angle between the vectors Vector U and Vector V.

6Given the vectors Vector U and Vector V, calculate:

1 The magnitudes of Vector U and ·

2 The cross product of Vector U and ·

3 The unit vector orthogonal to Vector Uand ·

4 The area of the parallelogram whose sides are the vectors Vector U and ·

7Calculate the triple product of: Triple Product Exercise if .

8Given the vectors Vector U, Vector V and Vector W, calculate the triple product Triple Product Exercise. Also, what is the volume of the parallelepiped whose edges are formed by these vectors?


1

Given the vectors Vector U, Vector V and Vector W, calculate the following:

1. Triple Product Problem, Triple Product Problem

Vector Calculations

Vector Solutions

2. Triple Product Problem, Triple Product Problem

Vector Calculations

Vector Solutions

3. Triple Product Problem

Vector Solution

4. Vector Magnitude Vector Magnitude

Vector Calculations

Vector Solution

5. Vector Cosine Exercise

Vector Solution


2

For what values of a do the vectors Basis Vector Exercise, Basis Vector Exercise and Basis Vector Exercise form a basis?

Vector Determinant

Vector Calculations

Vector Solutions

For a ≠ 1, the vectors form a basis.


3

Determining the value of the coefficient k for the vectors Vector X = kVector U − 2Vector V + 3Vector W, Vector Y = −Vector U + kVector V + Vector W if the vectors are:

1. Orthogonal.

Orthogonal Vectors

Vector Calculations

Vector Solution

2. Parallel.

Parallel Vectors

The system does not have a solution.


4

Find the direction cosines of the vector Direction Cosine Exercise.

Vector Magnitude

Vector Cosines


5

Calculate the angle between the vectors Angle between the Vectors Problem and Angle between the Vectors Exercise.

Vector Calculations

Vector Solutions


6

Given the vectors Vector Exercise and Vector Problems, calculate:

1 The magnitudes of Vector U and ·

Vector Magnitude Calculations

Vector Magnitude Solution

2 The cross product of Vector U and ·

Cross Product Calculations

3 The unit vector orthogonal to Vector Uand ·

Vector Product Operations

Unit Vector Solution

4 The area of the parallelogram whose sides are the vectors Vector U and ·

Vector Solution


7

Calculate the triple product of: Triple Product Exercise if .

Cross Product Calculations

Cross Product Operations

Cross Product Exercise

Cross Product Calculations

Cross Product Solution


8

Given the vectors Triple Product Exercises, Triple Product Problems and Vector Exercises, calculate the triple product Triple Product Word Problems. Also, what is the volume of the parallelepiped whose edges are formed by these vectors?

Triple Product Operations

Triple Product Solution