# Worksheet: Equation of a Straight Line in Space: Cartesian and Vector Forms

In this worksheet, we will practice finding the Cartesian and vector forms of the equation of a straight line in space.

**Q1: **

Find the direction vector of the straight line .

- A
- B
- C
- D
- E

**Q2: **

Find the Cartesian form of the equation of the straight line passing through the points and .

- A
- B
- C
- D

**Q3: **

Find the direction vector of the straight line .

- A
- B
- C
- D
- E

**Q4: **

Find the direction vector of the straight line .

- A
- B
- C
- D
- E

**Q5: **

Find the direction vector of the straight line .

- A
- B
- C
- D
- E

**Q6: **

Give the Cartesian equation of the line .

- A
- B
- C
- D

**Q7: **

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

**Q8: **

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

- A
- B
- C
- D

**Q9: **

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

- A
- B
- C
- D

**Q10: **

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

- A
- B
- C
- D

**Q11: **

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

- A
- B
- C
- D

**Q12: **

Find the direction cosines of the straight line whose direction ratio is .

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

**Q13: **

If the direction cosines of a straight line are , then find the possible values of .

- A,
- B3,
- C2,
- D,

**Q14: **

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

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

**Q15: **

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

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

**Q16: **

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

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

**Q17: **

Find the vector form of the equation of the straight line passing through the point and the center of the sphere whose equation is .

- A
- B
- C
- D

**Q18: **

Determine, in vector form, the equation of the straight line that passes through the points and .

- A
- B
- C
- D

**Q19: **

The points , , and form a triangle. Determine, in vector form, the equation of the median drawn from .

- A
- B
- C
- D

**Q20: **

Find the vector form of the equation of the straight line .

- A
- B
- C
- D