Worksheet: Cartesian Equation of a Straight Line in Space

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

Q1:

Find the direction vector of the straight line .

  • A
  • B
  • C
  • D
  • E

Q2:

The straight line that passes through the point 𝐴 ( 5 , 4 ) is perpendicular to the vector 𝑢 = ( 5 , 2 ) . Find the Cartesian equation of the line.

  • A 4 𝑥 5 𝑦 = 0
  • B 4 𝑥 5 𝑦 1 7 = 0
  • C 5 𝑥 2 𝑦 = 0
  • D 5 𝑥 2 𝑦 + 1 7 = 0

Q3:

Which of the following is a Cartesian equation for a straight line that passes through the point with direction vector ?

  • A
  • B
  • C
  • D

Q4:

Find the Cartesian form of the equation of the straight line passing through the points ( 7 , 3 , 7 ) and ( 3 , 1 0 , 4 ) .

  • A 𝑥 + 7 3 = 𝑦 + 3 7 = 𝑧 + 7 4
  • B 𝑥 4 7 = 𝑦 + 7 3 = 𝑧 3 7
  • C 𝑥 7 4 = 𝑦 3 7 = 𝑧 7 3
  • D 𝑥 + 7 4 = 𝑦 + 3 7 = 𝑧 + 7 3

Q5:

What is the equation of the line parallel to line 𝑥 1 0 2 = 𝑦 + 6 1 0 = 𝑧 + 2 6 and passing through ( 6 , 7 , 1 ) ?

  • A 𝑥 1 0 6 = 𝑦 + 6 7 = 𝑧 + 2 1
  • B 𝑥 + 6 2 = 𝑦 7 1 0 = 𝑧 + 1 6
  • C 𝑥 + 1 0 6 = 𝑦 6 7 = 𝑧 2 1
  • D 𝑥 6 2 = 𝑦 + 7 1 0 = 𝑧 1 6

Q6:

Find the direction vector of the straight line .

  • A
  • B
  • C
  • D
  • E

Q7:

Find the direction vector of the straight line .

  • A
  • B
  • C
  • D
  • E

Q8:

Find the direction vector of the straight line .

  • A
  • B
  • C
  • D
  • E

Q9:

Which of the following is a Cartesian equation for a straight line that passes through the point with direction vector ?

  • A
  • B
  • C
  • D

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