# Worksheet: Parallel and Perpendicular Vectors in Space

In this worksheet, we will practice recognizing parallel and perpendicular vectors in space.

**Q1: **

Determine whether the following is true or false: If the component of a vector in the direction of another vector is zero, then the two are parallel.

- Atrue
- Bfalse

**Q2: **

Given that , , and , find the relation between and .

- A
- B
- C
- D

**Q3: **

Given that , , and , where and are two perpendicular unit vectors, find the value of .

**Q4: **

Suppose , , , and , find .

- A
- B
- C
- D

**Q5: **

Given the two vectors and , determine whether these two vectors are parallel, perpendicular, or otherwise.

- Aparallel
- Bperpendicular
- Cotherwise

**Q7: **

In the figure, is perpendicular to the plane , which contains the points , , , and . If and , find the area of .

- A1,386
- B3,272.5
- C3,060
- D1,530

**Q8: **

Which of the following vectors is not perpendicular to the line whose direction vector is ?

- A
- B
- C
- D

**Q9: **

If the straight line is perpendicular to , and , find .

**Q10: **

If the straight line is parallel to , find .

**Q11: **

If the two straight lines and are perpendicular, find .

- A
- B
- C
- D

**Q12: **

Given that and satisfy , and . How are the two vectors related?

- Aperpendicular
- Bparallel