# Worksheet: Equation of a Straight Line in Space: Parametric Form

In this worksheet, we will practice finding the parametric equations of straight lines in space.

Q1:

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

Q2:

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

• A,
• B,
• C,
• D,

Q3:

Find the parametric equations of the straight line .

• A, ,
• B, ,
• C, ,
• D, ,

Q4:

Give the parametric equation of the line on point , with direction vector .

• A, ,
• B, ,
• C, ,
• D, ,

Q5:

Determine the parametric equations of the straight line passing through the points and .

• A, ,
• B, ,
• C, ,
• D, ,

Q6:

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

• A,
• B,
• C,
• D,

Q7:

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

• A,
• B,
• C,
• D,

Q8:

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

• A,
• B,
• C,
• D,

Q9:

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

• A,
• B,
• C,
• D,

Q10:

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

• A,
• B,
• C,
• D,

Q11:

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

• A,
• B,
• C,
• D,

Q12:

Which of the following are the parametric equations of the line through point with a direction perpendicular to vector ?

• A,
• B,
• C,
• D,

Q13:

Find the point of intersection of the lines and .

• A
• B
• C
• D
• E

Q14:

Find the point of intersection of the lines and .

• A
• B
• C
• Dno intersection point
• E

Q15:

Which of the following points lies on the straight line ?

• A
• B
• C
• D

Q16:

The line passes through the sphere . Find the length of the line segment between the two points of intersection of the line and the sphere. Give your answer to the nearest hundredth.

Q17:

A cube with side 3 sits with a vertex at the origin and three sides along the positive axes. Find the parametric equations of the main diagonal from the origin.

• A, ,
• B, ,
• C, ,
• D, ,

Q18:

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

Q19:

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

• A, ,
• B, ,
• C, ,
• D, ,