The portal has been deactivated. Please contact your portal admin.

Lesson Worksheet: Intersection of Planes Mathematics

In this worksheet, we will practice finding the points and lines of intersection between lines and planes in space.

Q1:

Which of the following is the direction vector of the line of intersection between the two planes 𝑥+3𝑦+𝑧2=0 and 𝑥+3𝑦3𝑧+2=0?

  • A310
  • B313
  • C313
  • D193
  • E310

Q2:

Find the vector equation of the line of intersection between the two planes 3𝑥+𝑦5𝑧=0 and 𝑥+2𝑦+𝑧+4=0.

  • A2.5,0,1.5+𝑡3,2,5
  • B1.5,0,2.5+𝑡11,8,5
  • C1.5,0,2.5+𝑡3,2,5
  • D2.5,0,1.5+𝑡11,8,5
  • E2.5,0,1.5+𝑡4,3,4

Q3:

Find the parametric equations of the line of intersection between the two planes 𝑥+𝑧=3 and 2𝑥𝑦𝑧=2.

  • A𝑥=3+𝑡, 𝑦=4+3𝑡, 𝑧=𝑡
  • B𝑥=3+𝑡, 𝑦=83𝑡, 𝑧=𝑡
  • C𝑥=3+𝑡, 𝑦=8+3𝑡, 𝑧=𝑡
  • D𝑥=1+𝑡, 𝑦=3+3𝑡, 𝑧=2𝑡
  • E𝑥=3+𝑡, 𝑦=43𝑡, 𝑧=𝑡

Q4:

Find the vector equation of the line of intersection between the two planes 𝑥+3𝑦+2𝑧6=0 and 2𝑥𝑦+𝑧+2=0.

  • Ar=0,2,12+𝑡5,3,7
  • Br=0,14,12+𝑡2,3,2
  • Cr=0,2,0+𝑡2,3,2
  • Dr=0,2,0+𝑡5,3,7
  • Er=0,14,12+𝑡5,3,7

Q5:

Which of the following points lies on the line of intersection of the two planes 9𝑥+16𝑦6𝑧11=0 and 13𝑥+2𝑦+4𝑧+1=0?

  • A(1,2,2)
  • B(1,2,2)
  • C(1,2,2)
  • D(1,3,2)
  • E(2,3,5)

Q6:

Find the point of intersection of the line 𝑥64=𝑦+3=𝑧 with the plane 𝑥+3𝑦+2𝑧6=0.

  • A(18,0,3)
  • B(10,2,1)
  • C(2,4,1)
  • D(2,4,1)
  • E(24,3,0)

Q7:

Find the coordinates of the point of intersection of the straight line r=8,2,5+𝑡7,9,13 with the plane 9,4,5=59r.

  • A(1,7,8)
  • B(6,8,14)
  • C(7,9,13)
  • D(1,7,8)
  • E(2,6,9)

Q8:

Find the point of intersection of the straight line 3𝑥=4𝑦2=𝑧+1 and the plane 3𝑥+𝑦+𝑧=13.

  • A(2,2,5)
  • B(2,2,5)
  • C(5,2,2)
  • D(2,5,2)

Q9:

Find the point of intersection of the planes 5𝑥2𝑦+6𝑧1=0, 7𝑥+8𝑦+𝑧6=0, and 𝑥3𝑦+3𝑧+11=0.

  • A(7,8,1)
  • B(5,2,6)
  • C(5,3,5)
  • D(1,3,3)
  • E(11,3,10)

Q10:

Find the point of intersection of the planes 4𝑥7𝑦7+2𝑧7=1, 𝑥+3𝑦+5𝑧16=0, and 2𝑥+3𝑦4𝑧9=0.

  • A(2,3,1)
  • B(2,3,1)
  • C(2,3,1)
  • D(2,3,1)
  • E(2,3,2)

This lesson includes 21 additional questions and 213 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.