Chapters

## Exercise 1

Find two unit vectors for and and determine the orthogonal vector for the two.

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## Exercise 2

Find a unit vector that is perpendicular to and .

## Exercise 3

Given the vectors and , find the product and verify that this vector is orthogonal to and . Also, find the vector and compare it with .

## Exercise 4

Consider the following figure:

Determine:

1 The coordinates of D if ABCD is a parallelogram.

## Exercise 5

Given the points and , determine:

1 What values of a are collinear.

2 Determine if values exist for a so that A, B, and C are three vertices of a parallelogram of area . If values do exist, determine the coordinates of C:

## Exercise 6

and are the three vertices of a triangle.

1. Calculate the cosine of each of the three angles in the triangle.

2. Calculate the area of the triangle.

## Solution of exercise 1

Find two unit vectors for and and determine the orthogonal vector for the two.

## Solution of exercise 2

Find a unit vector that is perpendicular to and .

## Solution of exercise 3

Given the vectors and , find the product and verify that this vector is orthogonal to and . Also, find the vector and compare it with .

## Solution of exercise 4

Consider the following figure:

Determine:

1 The coordinates of D if ABCD is a parallelogram.

## Solution of exercise 5

Given the points and , determine:

1 What values of a are collinear.

If A, B, and C are collinear, the vectors and  are linearly dependent and have proportional components.

2 Determine if values exist for a so that A, B, and C are three vertices of a parallelogram of area . If values do exist, determine the coordinates of C:

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## Solution of exercise 6

and are the three vertices of a triangle.

1. Calculate the cosine of each of the three angles in the triangle.

2. Calculate the area of the triangle.

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