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Lesson: Magnitude of a 2D Vector

Sample Question Videos

Worksheet • 25 Questions • 3 Videos

Q1:

Given that , find the value of .

Q2:

What is the magnitude of the vector οƒ  𝐴 𝐡 , where 𝐴 = ( 5 , βˆ’ 9 ) and 𝐡 = ( 9 , 1 ) ?

  • A 2 √ 2 9
  • B √ 1 4
  • C4
  • D116
  • E √ 1 0

Q3:

The vector ⃑ 𝑣 is shown on the grid of unit squares below. Find the value of β€– β€– ⃑ 𝑣 β€– β€– .

Q4:

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

Q5:

What is the difference between scalar quantities and vector quantities?

  • AVector quantities have both magnitude and direction; scalar quantities only have magnitude.
  • BScalar quantities have both magnitude and direction; vector quantities only have direction.
  • CScalar quantities have both magnitude and direction; vector quantities only have magnitude.
  • DScalar quantities only have direction; vector quantities only have magnitude.
  • EScalar quantities only have magnitude; vector quantities only have direction.

Q6:

Displacement is a vector quantity which combines distance and direction. For example, the displacement of Washington, DC, from New York City is 200 miles southwest.

What is the magnitude of the displacement?

  • A 200 miles
  • Bmiles southwest
  • C200
  • Dmiles
  • E 200 miles southwest

What is the direction of this displacement?

  • Asouthwest
  • Bmiles southwest
  • CNew York City
  • D 200 miles southwest
  • EWashington, DC

Q7:

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

  • A
  • B
  • C50
  • D
  • E7

Q8:

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

Q9:

Consider the vectors u = ⟨ 2 , 3 ⟩ and v = ⟨ 4 , 6 ⟩ .

What is the magnitude of u ? Give your answer correct to two decimal places if needed.

What is the magnitude of v ? Give your answer correct to two decimal places if needed.

What is the magnitude of u v + ? Give your answer correct to two decimal places if needed.

Q10:

What is the magnitude of the vector ?

Q11:

Given that , find the value of .

Q12:

The vector is shown on the grid of unit squares below. Find the value of .

  • A
  • B9
  • C
  • D5
  • E

Q13:

Which of the following is a direction vector for a line parallel to the 𝑦 -axis?

  • A ⃑ 𝑖 = ( 1 , 0 )
  • B ⃑ 𝑗 = ( 0 , 1 )

Q14:

Suppose the points 𝐴 and 𝐡 have coordinates ( π‘₯ , 𝑦 ) 1 1 and ( π‘₯ , 𝑦 ) 2 2 respectively. Find the magnitude of the vector οƒ  𝐴 𝐡 in terms of π‘₯ 1 , 𝑦 1 , π‘₯ 2 , and 𝑦 2 .

  • A  ( π‘₯ βˆ’ π‘₯ ) + ( 𝑦 βˆ’ 𝑦 ) 2 1 2 2 1 2
  • B √ 𝑦 βˆ’ 𝑦 2 1
  • C  ( π‘₯ βˆ’ π‘₯ ) 2 1 2
  • D √ π‘₯ βˆ’ π‘₯ 2 1
  • E  ( π‘₯ βˆ’ π‘₯ ) βˆ’ ( 𝑦 βˆ’ 𝑦 ) 2 1 2 2 1 2

Q15:

The vector is shown on the grid of unit squares below. Find the value of .

  • A
  • B
  • C
  • D13
  • E

Q16:

Water boils at 2 1 2 ∘ F . Is this temperature a scalar or vector quantity?

  • A vector
  • B scalar

The freezing point of water is 1 8 0 ∘ F lower than the boiling point of water. Is the freezing point of water a scalar or vector quantity?

  • A vector
  • B scalar

Q17:

An astronomer observes a comet through her telescope and notes down its location. Which additional piece of information would allow her to predict the position of the comet in an hour’s time?

  • Athe comet’s velocity
  • Bthe comet’s speed
  • Cthe comet’s displacement relative to her
  • Dthe comet’s distance from her

Q18:

Given that ⃑ 𝐴 = ( 2 , 1 4 ) , find β€– β€– ⃑ 𝐴 β€– β€– .

  • A 1 0 √ 2
  • B200
  • C 3 √ 2
  • D4

Q19:

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

Q20:

The vector is shown on the grid of unit squares below. Find the value of .

Q21:

Given that ⃑ 𝐴 = βˆ’ 5 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 , where ⃑ 𝑖 and ⃑ 𝑗 are two perpendicular unit vectors, find β€– β€– ⃑ 𝐴 β€– β€– .

  • A √ 3 4
  • B 2 √ 2
  • C 2 √ 7
  • D √ 1 4

Q22:

The vector is shown on the grid of unit squares below. Find the value of .

Q23:

What is the magnitude of the vector ?

Q24:

Adel is 25 years old. Is his age a scalar or vector quantity?

  • A vector
  • B scalar

Adel’s father is 31 years older than him. Is his father’s age a scalar or vector quantity?

  • A vector
  • B scalar

Q25:

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

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