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Worksheet: Direction Cosines of a Straight Line

Q1:

Find the direction cosines of the straight line whose direction ratio is 2 1 1 .

  • A 2 , 2 2 , 2 2 , 2 , 2 2 , 2 2
  • B 1 3 , 1 3 , 1 3 , 1 3 , 1 3 , 1 3
  • C 2 2 , 2 , 2 , 2 2 , 2 , 2
  • D 6 3 , 6 6 , 6 6 , 6 3 , 6 6 , 6 6
  • E 1 , 1 2 , 1 2 , 1 , 1 2 , 1 2

Q2:

Find the direction cosines of the straight line whose direction ratio is 4 5 2 .

  • A 4 7 7 , 5 7 7 , 2 7 7 , 4 7 7 , 5 7 7 , 2 7 7
  • B 4 4 5 , 4 4 5 , 4 4 5 , 4 4 5 , 4 4 5 , 4 4 5
  • C 4 7 , 5 7 , 2 7 , 4 7 , 5 7 , 2 7
  • D 4 5 1 5 , 5 3 , 2 5 1 5 , 4 5 1 5 , 5 3 , 2 5 1 5
  • E 4 7 , 5 7 , 2 7 , 4 7 , 5 7 , 2 7

Q3:

If the direction cosines of a straight line are 1 𝑐 , 1 𝑐 , 1 𝑐 , then find the possible values of 𝑐 .

  • A3, 3
  • B 2 , 2
  • C2, 2
  • D 3 , 3

Q4:

Find the direction cosines of the normal to the plane 4 𝑥 + 8 𝑦 3 𝑧 = 2 8 .

  • A 1 4 , 1 2 , 3 1 6
  • B 4 1 5 1 5 , 8 1 5 1 5 , 1 5 5
  • C 4 8 9 , 8 8 9 , 3 8 9
  • D 4 8 9 8 9 , 8 8 9 8 9 , 3 8 9 8 9

Q5:

Find the direction cosines of the normal to the plane 8 𝑥 + 5 𝑦 2 𝑧 = 6 .

  • A 1 8 , 5 6 4 , 1 3 2
  • B 8 1 5 1 5 , 1 5 3 , 2 1 5 1 5
  • C 8 9 3 , 5 9 3 , 2 9 3
  • D 8 9 3 9 3 , 5 9 3 9 3 , 2 9 3 9 3

Q6:

Find the direction cosines of the normal to the plane 6 𝑥 + 7 𝑦 + 3 𝑧 = 6 .

  • A 1 6 , 7 3 6 , 1 1 2
  • B 3 2 , 7 4 , 3 4
  • C 3 4 7 , 7 9 4 , 3 9 4
  • D 3 9 4 4 7 , 7 9 4 9 4 , 3 9 4 9 4

Q7:

Given that 𝑙 , 𝑚 , and 𝑛 are the direction cosines of a straight line, find the value of 𝑙 + 𝑚 + 𝑛 2 2 2 .

Q8:

If the direction angles of a straight line are , , and , then find the value of .

Q9:

Which of the following gives the direction cosines of a straight line?

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

Q10:

Suppose that | | = 6 A and A has direction cosines 2 3 , 2 3 , and 1 3 . Determine A B × , where B = 8 , 0 , 3 .

  • A 3 2 1 2 + 4 i j k
  • B 1 2 4 3 2 i j k
  • C 1 2 + 2 8 + 3 2 i j k
  • D 1 2 + 4 3 2 i j k

Q11:

The given figure represents a vector whose norm is 5 units. Find the size of the direction angles of approximated to one decimal place.

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