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Lesson: Finding the Equation and the Direction Vector of a Straight Line in Three Dimensions

Worksheet: Finding the Equation and the Direction Vector of a Straight Line in Three Dimensions • 22 Questions

Q1:

Give the Cartesian equation of the line through point and with direction vector .

  • A
  • B
  • C
  • D

Q2:

Give the Cartesian equation of the line through point and with direction vector .

  • A
  • B
  • C
  • D

Q3:

Give the Cartesian equation of the line through point and with direction vector .

  • A
  • B
  • C
  • D

Q4:

Find the direction vector of the straight line .

  • A
  • B
  • C
  • D
  • E

Q5:

Find the direction vector of the straight line .

  • A
  • B
  • C
  • D
  • E

Q6:

Find the Cartesian form of the equation of the straight line passing through the point and makes equal angles with the coordinates axes.

  • A
  • B
  • C
  • D

Q7:

Find the Cartesian form of the equation of the straight line passing through the point and makes equal angles with the coordinates axes.

  • A
  • B
  • C
  • D

Q8:

What is the equation of the line parallel to line and passing through ?

  • A
  • B
  • C
  • D

Q9:

Determine the parametric equations of the straight line passing through the points and .

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q10:

Determine the parametric equations of the straight line passing through the points and .

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q11:

If the straight line is parallel to , find .

Q12:

If the straight line is parallel to , find .

Q13:

Given that the lines and are perpendicular, what is ?

Q14:

Given that the lines and are perpendicular, what is ?

Q15:

Suppose that lines and are parallel, what are and ?

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

Q16:

Suppose that lines and are parallel, what are and ?

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

Q17:

Given that the vector is parallel to the line , find .

Q18:

Given that the vector is parallel to the line , find .

Q19:

For what values of is the line parallel to the line ?

Q20:

If the straight line is perpendicular to , and , find .

Q21:

If the two straight lines and are perpendicular, find .

  • A
  • B
  • C
  • D

Q22:

Given that is perpendicular to , what is ?

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