# Worksheet: Equations of Parallel and Perpendicular Lines in Space

In this worksheet, we will practice finding the equation of a straight line that is parallel or perpendicular to another one in space and finding the intersection point between two lines.

Q1:

The straight line that passes through the point is perpendicular to the vector . Find the Cartesian equation of the line.

• A
• B
• C
• D

Q2:

What is the equation of the line parallel to line and passing through ?

• A
• B
• C
• D

Q3:

Find the Cartesian form of the equation of the straight line passing through the origin and the intersection point of the two straight lines and , .

• A
• B
• C
• D

Q4:

Find the vector form of the equation of the straight line passing throught the point and parallel to the straight line passing through the two points and .

• A
• B
• C
• D

Q5:

Find the vector form of the equation of the straight line passing through the point and the intersection point of the two straight lines and .

• A
• B
• C
• D

Q6:

Determine the vector form of the equation of the straight line passing through the point and parallel to the vector .

• A
• B
• C
• D

Q7:

Given that is perpendicular to , what is ?

Q8:

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

Q9:

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, ,

Q10:

Suppose that lines and are parallel, what are and ?

• A,
• B,
• C,
• D,
• E,

Q11:

Given that the lines and are perpendicular, what is ?

Q12:

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

• A
• B
• C
• D

Q13:

For what value of do the lines and intersect?

Q14:

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