Lesson Worksheet: Equation of a Straight Line in Space: Cartesian and Vector Forms Mathematics

In this worksheet, we will practice finding the Cartesian and vector forms of the equation of a straight line in space.

Q1:

Find the direction vector of the straight line 𝑥16=𝑦64=𝑧83.

  • A(6,4,3)
  • B(1,6,8)
  • C(6,4,3)
  • D(1,6,8)
  • E(1,6,8)

Q2:

Find the Cartesian form of the equation of the straight line passing through the points (7,3,7) and (3,10,4).

  • A𝑥+74=𝑦+37=𝑧+73
  • B𝑥+73=𝑦+37=𝑧+74
  • C𝑥74=𝑦37=𝑧73
  • D𝑥47=𝑦+73=𝑧37

Q3:

Give the Cartesian equation of the line r=3,2,2+𝑡4,2,4.

  • A𝑥+34=𝑦+22=𝑧+24
  • B𝑥43=𝑦22=𝑧42
  • C𝑥+43=𝑦+22=𝑧+42
  • D𝑥34=𝑦+22=𝑧+24

Q4:

Find the Cartesian form of the equation of the straight line passing through the point (4,1,2) and makes equal angles with the coordinates axes.

  • A𝑥4=𝑦1=𝑧2
  • B𝑥+43=𝑦13=𝑧23
  • C𝑥14=𝑦11=𝑧12
  • D𝑥+41=𝑦11=𝑧21

Q5:

Give the Cartesian equation of the line through point (2,5,2) and with direction vector 3,5,4.

  • A𝑥+23=𝑦55=𝑧24
  • B𝑥32=𝑦+55=𝑧+42
  • C𝑥+32=𝑦55=𝑧42
  • D𝑥23=𝑦+55=𝑧+24

Q6:

Give the vector equation of the line through the point (3,7,7) with direction vector 0,5,7.

  • Ar=3,7,7+𝑡0,5,7
  • Br=0,5,7+𝑡3,7,7
  • Cr=3,7,7+𝑡3,7,7
  • Dr=0,5,7+𝑡0,5,7

Q7:

Find the direction vector of the straight line passing through 𝐴1,2,7 and 𝐵4,1,3.

  • Ad=3,1,4
  • Bd=5,3,10
  • Cd=3,1,4
  • Dd=3,1,4

Q8:

Give a direction vector of the line through the origin and the point (6,6,1).

  • Ad=6,6,1
  • Bd=6,6,1
  • Cd=0,0,0
  • Dd=6,6,1

Q9:

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

  • A𝑥=0, 𝑧=0
  • B𝑥=0, 𝑦=0
  • C𝑧=0
  • D𝑥=1
  • E𝑧=1

Q10:

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

  • A𝑦=0, 𝑧=0
  • B𝑧=1
  • C𝑥=1
  • D𝑦=0, 𝑥=0
  • E𝑥=0

This lesson includes 21 additional questions and 216 additional question variations for subscribers.

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