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Worksheet: Direction Angles and Direction Cosines

Q1:

Suppose that 3 1 ∘ , 6 5 ∘ and πœƒ are the direction angles of a vector. Which of the following, to the nearest hundredth, is πœƒ ?

  • A 2 6 4 . 0 0 ∘
  • B 8 4 . 0 0 ∘
  • C 8 5 . 0 3 ∘
  • D 7 2 . 8 8 ∘

Q2:

Find the direction cosines of the vector .

  • A
  • B
  • C
  • D

Q3:

Determine the angle between the vectors and in ℝ 3 .

  • A πœ‹ 2
  • B √ 3 2
  • C0
  • D a r c c o s ο€Ώ √ 3 2 

Q4:

Find the vector of norm 61 and direction cosines .

  • A
  • B
  • C
  • D
  • E

Q5:

Find the vector of norm 59 and direction cosines .

  • A
  • B
  • C
  • D
  • E

Q6:

Find the algebraic form of a vector if its norm is 31, given that it makes equal angles with the positive directions of the Cartesian axes.

  • A
  • B
  • C

Q7:

If , find the size of the angle that makes with the positive direction of the -axis approximated to the nearest second.

  • A
  • B
  • C
  • D

Q8:

Find the direction angles of the vector .

  • A
  • B
  • C
  • D
  • E

Q9:

Find, to the nearest second, the size of the angle that vector A = ⟨ βˆ’ 9 , 4 , 8 ⟩ makes with the π‘₯ -axis.

  • A 5 0 5 4 β€² 5 0 β€² β€² ∘
  • B 7 1 3 7 β€² 2 8 β€² β€² ∘
  • C 1 3 5 1 0 β€² 4 1 β€² β€² ∘

Q10:

The direction angles of are , , and . Which of the following planes contains ?

  • A
  • B
  • C

Q11:

The direction angles of are , , and . Which of the following planes contains ?

  • A
  • B
  • C

Q12:

The direction angles of are , , and . Which of the following planes contains ?

  • A
  • B
  • C

Q13:

Find vector whose norm is 41 and whose direction angles are .

  • A
  • B
  • C
  • D

Q14:

Find the size of the direction angles of the vector , represented by the given figure, corrected to one decimal place.

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

Q15:

Find the direction cosines of the vector that lies in the positive coordinate plane π‘₯ 𝑧 and makes an angle of 6 0 ∘ with the positive 𝑧 -axis.

  • A ο€Ώ √ 3 2 , 1 2 , 0 
  • B ο€Ώ 0 , √ 3 2 , 1 2 
  • C ο€Ώ 1 2 , 0 , √ 3 2 
  • D ο€Ώ √ 3 2 , 0 , 1 2 
  • E ο€Ώ 0 , 1 2 , √ 3 2 