# Solutions to Problem Set 2

Math 311-01/02

1-26-2018

[Vectors]

1. Vectors and are shown below.

Sketch the vectors , , and .

[Dot product]

2. Compute the dot product .

3. Compute the dot product .

We won't be using dot products in dimensions other than 2 or 3 in this course. The point of this problem is to show that it doesn't work any differently with higher-dimensional vectors.

4. Compute the dot product .

5. Find the exact value of the cosine of the angle between and .

Tell whether the vectors are orthogonal; if not, tell whether the angle between them is acute or obtuse.

The angle is acute.

6. Find the exact value of the cosine of the angle between and .

Tell whether the vectors are orthogonal; if not, tell whether the angle between them is acute or obtuse.

The vectors are orthogonal.

7. Find the exact value of the cosine of the angle between and .

Tell whether the vectors are orthogonal; if not, tell whether the angle between them is acute or obtuse.

The angle is obtuse.

8. Find the scalar component of in the direction of .

9. Find the scalar component of in the direction of .

10. Find the vector component of in the direction of .

11. Find the vector component of in the direction of .

We spend time envying people whom we wouldn't wish to be. - Jean Rostand

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