Lesson Worksheet: The Perpendicular Distance between Points and Planes Mathematics

Start Practising

In this worksheet, we will practice calculating the perpendicular distance between a plane and a point, between a plane and a straight line parallel to it, and between two parallel planes using a formula.

Q1:

Find the distance between the point (2,−1,3) and the plane r⋅⟨−2,2,1⟩=3.

  • A1length unit
  • B13length units
  • C23length units
  • D2length units

Q2:

Find the distance between the point (−5,−8,−6) and the plane −2𝑥+𝑦+2𝑧=7.

  • A17125 length units
  • B179 length units
  • C173 length units
  • D17 length units

Q3:

Find, to the nearest two decimal places, the distance between the point (3,2,3) and the plane 2(𝑥−2)+3(𝑦−3)+(𝑧−1)=0.

Q4:

Which of the following is the distance of the point (3,−4,5) from the plane 4𝑥21+8𝑦21+5𝑧21=1 rounded to two decimal places?

  • A1.56
  • B0.39
  • C6.10
  • D3.88
  • E0.64

Q5:

Find the perpendicular distance between the line r=⟨1,2,4⟩+𝑡⟨−2,1,4⟩ and the plane r⟨2,0,1⟩=1.

  • A10
  • B√5
  • C5
  • D√10
  • E2√5

Q6:

Find the distance between the line 𝑥−12=𝑦−24=𝑧+52 and the plane 3𝑥−2𝑦+𝑧=−2. Give your answer to one decimal place.

Q7:

Find the distance between the two planes −𝑥−2𝑦−2𝑧=−2 and −2𝑥−4𝑦−4𝑧=3.

  • A710length unit
  • B76length units
  • C25length unit
  • D23length unit

Q8:

Find, to the nearest two decimal places, the distance between the two planes 2(𝑥−2)+(𝑦−3)+3(𝑧−1)=0 and r⋅⟨4,2,6⟩=12.

Q9:

Find, to the nearest hundredth, the distance between the two planes 𝑥+2𝑦+4𝑧=4 and 2𝑥13+4𝑦13+8𝑧13=1.

Q10:

Find, to the nearest hundredth, the distance between the two planes ⟨6,3,6⟩⋅=11r and 𝑥3+𝑦6+𝑧3=1.

This lesson includes 20 additional questions and 243 additional question variations for subscribers.

GET YOUR PORTAL NOW

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