# Worksheet: Equation of a Straight Line in Three Dimensions

In this worksheet, we will practice finding the direction vector and the equation of a straight line in three dimensions.

**Q1: **

Suppose that lines and are parallel, what are and ?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q2: **

For what values of is the line parallel to the line ?

**Q3: **

Give the Cartesian equation of the line through point and with direction vector .

- A
- B
- C
- D

**Q4: **

Find the Cartesian form of the equation of the straight line passing through the point and makes equal angles with the coordinates axes.

- A
- B
- C
- D

**Q5: **

Given that the lines and are perpendicular, what is ?

**Q6: **

Given that the vector is parallel to the line , find .

**Q7: **

Given that is perpendicular to , what is ?

**Q8: **

Give the parametric equation of the line through the origin with direction vector .

- A , ,
- B , ,
- C , ,
- D , ,

**Q9: **

Give the equations for the -axis in 3-dimensional space.

- A
- B ,
- C
- D ,
- E

**Q10: **

Give the equations for the -axis in 3-dimensional space.

- A
- B ,
- C
- D ,
- E

**Q11: **

Which of the following is a directional vector for a line perpendicular to the -axis?

- A
- B

**Q12: **

Find the parametric equations of the straight line that passes through the point and that is parallel to the bisector of the second quadrant of the plane .

- A , ,
- B , ,
- C , ,
- D , ,

**Q13: **

Write the equation of the straight line passing through the points and in parametric form.

- A , , , for
- B , , , for
- C , , , for
- D , , , for
- E , , , for

**Q14: **

Which of the following is a direction vector of the straight line ?

- A
- B
- C
- D
- E

**Q15: **

Find the equation of the line through the origin that intersects the line orthogonally.

- A
- B
- C
- D

**Q16: **

Give the vector equation of the line through the point with direction vector .

- A
- B
- C
- D

**Q17: **

Find the direction vector of the straight line passing through and .

- A
- B
- C
- D

**Q18: **

Give a direction vector of the line through the origin and the point .

- A
- B
- C
- D

**Q19: **

For what value of do the lines and intersect?

**Q20: **

Give equations for the -axis in 3-dimensional space.

- A
- B ,
- C
- D ,
- E