# Worksheet: Inner Products of Vectors

In this worksheet, we will practice performing inner product in Rⁿ and using it to find the magnitude of a vector, angle, or distance between two vectors.

**Q1: **

Given that and , find the distance between and .

- A
- B
- C
- D
- E

**Q2: **

Given that , find .

**Q3: **

Given that are orthogonal vectors, complete the following comparison statement: .

- A
- B
- C
- D
- E

**Q4: **

Given and , find .

**Q5: **

Given that , complete the following comparison statement: .

- A
- B
- C
- D
- E

**Q6: **

Given , complete the following comparison statement: .

- A
- B
- C
- D
- E

**Q7: **

Given that and , are and orthogonal?

- AYes
- BNo

**Q8: **

Given that , where , , find the angle between the vectors and in degrees, rounded to the nearest 3 decimal places.

**Q9: **

True or False: only if is the zero vector.

- ATrue
- BFalse

**Q10: **

Given that and that , find the value of .

- A1
- B2
- C
- D4
- E