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Worksheet: Scalars, Vectors, and Directed Line Segments

Q1:

Which vector has the same direction as ?

  • A
  • B
  • C

Q2:

In the given parallelogram 𝐴 𝐡 𝐢 𝐷 , 𝐴 𝐢 ∩ 𝐡 𝐷 = { 𝑀 } , 𝐸 is the midpoint of 𝐴 𝐡 , and 𝐹 is the midpoint of 𝐡 𝐢 . Complete the following: 1 2 οƒ  𝐴 𝐢 is equivalent to .

  • A οƒ  𝐷 𝑀
  • B οƒ  𝑀 𝐴
  • C οƒ  𝑀 𝐷
  • D οƒ  𝐴 𝑀

Q3:

Find the components of the vector ⃑ 𝑣 shown on the grid of unit squares below.

  • A ( 0 , βˆ’ 6 )
  • B ( 0 , 6 )
  • C ( βˆ’ 6 , 0 )
  • D ( 6 , 0 )
  • E ( 6 , 1 )

Q4:

Find the magnitude of the vector ⃑ 𝑣 shown on the grid of unit squares below.

Q5:

Find the magnitude of the vector shown on the grid of unit squares below.

  • A
  • B
  • C5
  • D
  • E9

Q6:

Find the magnitude of the vector shown on the grid of unit squares below.

  • A
  • B
  • C13
  • D
  • E

Q7:

Given that οƒŸ 𝑀 = ο€Ό 5 2 , 2  , express the vector οƒŸ 𝑀 in terms of the unit vectors ⃑ 𝑖 and ⃑ 𝑗 , and find its norm β€– β€– οƒŸ 𝑀 β€– β€– .

  • A οƒŸ 𝑀 = 5 2 ⃑ 𝑖 + 2 ⃑ 𝑗 , β€– β€– οƒŸ 𝑀 β€– β€– = 3 √ 2 2
  • B οƒŸ 𝑀 = 2 ⃑ 𝑖 + 5 2 ⃑ 𝑗 , β€– β€– οƒŸ 𝑀 β€– β€– = √ 4 1 2
  • C οƒŸ 𝑀 = βˆ’ 5 2 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 , β€– β€– οƒŸ 𝑀 β€– β€– = √ 4 1 2
  • D οƒŸ 𝑀 = 5 2 ⃑ 𝑖 + 2 ⃑ 𝑗 , β€– β€– οƒŸ 𝑀 β€– β€– = √ 4 1 2
  • E οƒŸ 𝑀 = βˆ’ 5 2 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 , β€– β€– οƒŸ 𝑀 β€– β€– = 3 √ 2 2

Q8:

Given that ⃑ 𝐴 = βˆ’ 9 ⃑ 𝑖 βˆ’ 7 ⃑ 𝑗 , where ⃑ 𝑖 and ⃑ 𝑗 are two perpendicular unit vectors, find βˆ’ 1 2 ⃑ 𝐴 .

  • A 9 2 ⃑ 𝑖 βˆ’ 7 ⃑ 𝑗
  • B 7 2 ⃑ 𝑖 + 9 2 ⃑ 𝑗
  • C βˆ’ 9 ⃑ 𝑖 + 7 2 ⃑ 𝑗
  • D 9 2 ⃑ 𝑖 + 7 2 ⃑ 𝑗

Q9:

Given that the vectors and are perpendicular, find the value of .

Q10:

Given that 𝐴 𝐡 𝐢 𝐷 is a square of side length 9 cm, determine the scalar product of ο€Ί 2 οƒ  𝐷 𝐡  and ο€Ό 3 5 οƒ  𝐡 𝐴  .

Q11:

Given that is a rectangle in which cm and cm, define the algebraic projection of in the direction of .

Q12:

If 𝐴 𝐡 𝐢 𝐷 is a rectangle in which 𝐴 𝐡 = 1 0 c m and 𝐡 𝐢 = 6 c m , evaluate ο€Ό βˆ’ 1 2 οƒ  𝐡 𝐷  βŠ™ ο€Ό 1 2 οƒŸ 𝐡 𝐢  .

Q13:

If 𝐴 𝐡 𝐢 𝐷 is a rhombus in which 𝐴 𝐢 = 1 5 c m and 𝐡 𝐷 = 2 0 c m , evaluate ο€Ό 7 1 0 οƒ  𝐷 𝐢  βŠ™ ο€Ό 3 5 οƒ  𝐴 𝐢  .