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# Worksheet: Equation of a Straight Line in Three Dimensions

Q1:

Given that is perpendicular to , what is ?

Q2:

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

Q3:

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

Q4:

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 , ,

Q5:

Suppose that lines and are parallel, what are and ?

• A ,
• B ,
• C ,
• D ,
• E ,

Q6:

Suppose that lines and are parallel, what are and ?

• A ,
• B ,
• C ,
• D ,
• E ,

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:

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

Q9:

Given that the lines and are perpendicular, what is ?

Q10:

Given that the lines and are perpendicular, what is ?

Q11:

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

Q12:

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

• A
• B
• C
• D

Q13:

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

• A
• B
• C
• D

Q14:

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

• A
• B
• C
• D

Q15:

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

• A , ,
• B , ,
• C , ,
• D , ,

Q16:

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

Q17:

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

• A
• B ,
• C
• D ,
• E

Q18:

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

• A
• B
• C
• D
• E

Q19:

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

• A
• B

Q20:

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

• A
• B ,
• C
• D ,
• E