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