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Lesson: Vector Projection

Worksheet • 15 Questions

Q1:

Consider the points 𝐴 ( 5 , βˆ’ 1 , βˆ’ 8 ) and 𝐡 ( βˆ’ 3 , βˆ’ 9 , βˆ’ 6 ) . Find the component of the vector V i j k = βˆ’ 5 βˆ’ 2 + 2 in the direction  𝐴 𝐡 rounded to the nearest hundredth.

Q2:

Consider the points 𝐴 ( 7 , βˆ’ 6 , 0 ) and 𝐡 ( βˆ’ 5 , βˆ’ 7 , βˆ’ 4 ) . Find the component of the vector V i j k = βˆ’ 8 βˆ’ 9 βˆ’ 3 in the direction  𝐴 𝐡 rounded to the nearest hundredth.

Q3:

Consider the points 𝐴 ( βˆ’ 6 , 7 , 3 ) and 𝐡 ( βˆ’ 7 , βˆ’ 5 , βˆ’ 2 ) . Find the component of the vector V i j = 5 βˆ’ 9 in the direction  𝐴 𝐡 rounded to the nearest hundredth.

Q4:

Given that is a square having a side length of 53 cm, calculate the algebraic projection of in the direction of .

Q5:

𝐴 𝐡 𝐢 𝐷 is a trapezium, where  𝐴 𝐷 βˆ₯ οƒͺ 𝐡 𝐢 , π‘š ∠ 𝐴 = π‘š ∠ 𝐡 = 9 0 ∘ , π‘š ∠ 𝐢 = 6 0 ∘ , 𝐴 𝐷 = 6 0 c m , and 𝐡 𝐢 = 1 0 1 c m . Determine the algebraic projection of οƒ  𝐢 𝐷 on the direction of οƒŸ 𝐢 𝐡 .

Q6:

Determine whether the following is true or false: If the component of a vector in the direction of another vector is zero, then the two are perpendicular.

  • Afalse
  • Btrue

Q7:

is a right-angled triangle in which , and . Determine the algebraic projection of in the direction of .

  • A28
  • B
  • C
  • D22.4

Q8:

is a right-angled triangle in which , and . Determine the algebraic projection of in the direction of .

  • A8
  • B
  • C
  • D3.76

Q9:

Given that the measure of the smaller angle between ⃑ 𝐴 and ⃑ 𝐡 is 1 5 0 ∘ , and β€– β€– ⃑ 𝐡 β€– β€– = 5 4 , determine the component of vector ⃑ 𝐡 along ⃑ 𝐴 .

  • A βˆ’ 2 7 √ 3
  • B27
  • C54
  • D βˆ’ 1 8 √ 3

Q10:

If β€– β€– ⃑ 𝐴 β€– β€– = 5 , | | ⃑ 𝐡 | | = 1 5 , and the measure of the angle between them is 3 0 ∘ , find the algebraic projection of ⃑ 𝐡 in the direction of ⃑ 𝐴 .

  • A 1 5 √ 3 2
  • B 1 5 2
  • C 5 2
  • D 7 5 √ 3 2
  • E 5 √ 3 2

Q11:

Determine, to the nearest hundredth, the component of vector ⃑ 𝑉 along οƒ  𝐴 𝐡 , given that ⃑ 𝑉 = ( βˆ’ 7 , 2 , 1 0 ) and the coordinates of 𝐴 and 𝐡 are ( 1 , βˆ’ 4 , βˆ’ 8 ) and ( 3 , 2 , 0 ) , respectively.

Q12:

Determine, to the nearest hundredth, the component of vector ⃑ 𝑉 along οƒ  𝐴 𝐡 , given that ⃑ 𝑉 = ( 5 , 7 , βˆ’ 9 ) and the coordinates of 𝐴 and 𝐡 are ( βˆ’ 1 , βˆ’ 3 , βˆ’ 5 ) and ( βˆ’ 3 , βˆ’ 1 0 , βˆ’ 9 ) , respectively.

Q13:

Find the component of vector ⃑ 𝐴 in the direction of ⃑ 𝐡 , where πœƒ is the included angle between them.

  • A β€– β€– ⃑ 𝐴 β€– β€– πœƒ c o s
  • B β€– β€– ⃑ 𝐴 β€– β€– Γ— ⃑ 𝐡 πœƒ c o s
  • C ο€Ί ⃑ 𝐴 β‹… ⃑ 𝐡  πœƒ c o s
  • D β€– β€– ⃑ 𝐴 β€– β€– Γ— ⃑ 𝐡 πœƒ c o s
  • E β€– β€– ⃑ 𝐡 β€– β€– πœƒ c o s

Q14:

Determine the magnitude of the component of F i j = 2 3 + 1 7 in the direction of  𝐴 𝐡 , given that the coordinates of the points 𝐴 and 𝐡 are ( 2 , 3 ) and ( 6 , 6 ) respectively.

  • A28.6
  • B27.4
  • C8.2
  • D0.2

Q15:

Given that ⃑ 𝐴 = ( βˆ’ 6 , 3 , βˆ’ 2 ) and ⃑ 𝐡 = ( 4 , 1 , 6 ) , determine the component of ⃑ 𝐴 along ⃑ 𝐡 .

  • A βˆ’ 3 3 √ 5 3 5 3
  • B βˆ’ 3 3 7
  • C 6 7
  • D βˆ’ 5 √ 5 3 5 3
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