# Worksheet: Intersection of Planes

In this worksheet, we will practice finding the point/line of intersection between planes given their equations.

Q1:

Find the point of intersection of the planes , , and .

• A
• B
• C
• D
• E

Q2:

Find the point of intersection of the planes , , and .

• A
• B
• C
• D
• E

Q3:

Find the point of intersection of the planes , , and .

• A
• B
• C
• D
• E

Q4:

Find the point of intersection of the planes , , and .

• A
• B
• C
• D
• E

Q5:

Find the point of intersection of the planes , , and .

• A
• B
• C
• D
• E

Q6:

Find the coordinates of the point of intersection of the straight line with the plane .

• A
• B
• C
• D
• E

Q7:

Straight line is parallel to plane , and from a point neither on the line nor in the plane are drawn rays , meeting in and . If , what is the ratio between and ?

• A
• B
• C
• D

Q8:

Find the point of intersection of the straight line and the plane .

• A
• B
• C
• D

Q9:

Determine whether the following sentence is true or false: In every plane, any two intersecting lines are perpendicular.

• Atrue
• Bfalse

Q10:

Find the point of intersection of the planes , , and .

• A
• B
• C
• D
• E

Q11:

Which of the following is the direction vector of the line of intersection between the two planes and ?

• A
• B
• C
• D
• E

Q12:

Find the parametric equations of the line of intersection between the two planes and .

• A, , and
• B, , and
• C, , and
• D, , and
• E, , and

Q13:

Consider three intersecting planes. The normals to each of the planes are coplanar. Are the lines of intersection parallel?

• ANo
• BYes

Q14:

Find the vector equation of the line of intersection between the two planes and .

• A
• B
• C
• D
• E

Q15:

Find the point of intersection of the line with the plane .

• A
• B
• C
• D
• E

Q16:

Find the vector equation of the line of intersection between the two planes and .

• A
• B
• C
• D
• E