Worksheet: Addition and Subtraction of Vectors

In this worksheet, we will practice adding and subtracting vectors in 2D.

Q1:

Given that A = 1 , 9 and B = 4 , 1 , find A B .

  • A 5 , 8
  • B 3 , 1 0
  • C 1 0 , 3
  • D 8 , 5
  • E 8 , 5

Q2:

Given that A = 9 , 5 , B = 1 0 , 3 , and C = 3 , 6 , find A B C + .

  • A 2 2 , 4
  • B 4 , 1 4
  • C 2 2 , 4
  • D 2 , 2
  • E 1 6 , 8

Q3:

Given that A = 2 , 2 , B = 5 , 2 , and C = 3 , 2 , find + A B C .

  • A 0 , 2
  • B 0 , 2
  • C 1 0 , 2
  • D 4 , 2

Q4:

Given that A = 1 , 2 and B = 3 , 6 , find 6 + 2 A B .

  • A 1 2 , 0
  • B 1 2 , 0
  • C 0 , 2 4
  • D 0 , 0
  • E 0 , 2 4

Q5:

A woman started walking from home and walked 6 miles at 4 0 north of east, then 2 miles at 1 5 east of south, then 5 miles at 3 0 south of west. If she walked straight home, how far would she have to walk and in what direction? Give the distance in miles correct to 2 decimal places and the direction in degrees correct to one decimal place.

  • A 1.93 miles, 5 6 . 6 west of north
  • B 6.06 miles, 8 6 . 2 north of west
  • C 0.97 miles, 3 6 . 3 north of west
  • D 6.06 miles, 8 6 . 2 west of north
  • E 1.93 miles, 2 7 . 5 east of north

Q6:

Given that B = 9 , 3 , C = 4 , 2 , and D = 2 , 9 , determine the vector A that satisfies the equation A B C D = 4 + 2 6 .

  • A 4 0 , 4 6
  • B 4 0 , 4 6
  • C 5 6 , 3 8
  • D 5 6 , 3 8

Q7:

Given that A = 9 , 1 2 and B = 1 3 , 1 , find A B + .

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

Q8:

If = 5 u and = 2 v , what is the smallest that + u v could be?

Q9:

Are there any vector u and v for which + > + u v u v ?

  • Ano
  • Byes

Q10:

Let u = 3 , 2 and v = 9 , 5 .

What are the components of u v + ?

  • A 3 , 6
  • B 8 , 1 1
  • C 1 2 , 7
  • D 6 , 3
  • E 2 7 , 1 0

What are the components of v u + ?

  • A 8 , 1 1
  • B 1 2 , 7
  • C 6 , 3
  • D 3 , 6
  • E 2 7 , 1 0

Q11:

Consider the vectors u = 1 , 2 and v = 3 , 1 .

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 if needed.

Q12:

Consider the vectors u = 5 , 2 and v = 5 , 2 .

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.

Q13:

Given that A i j = 5 + 1 0 and B i j = 4 5 , where i and j are two perpendicular unit vectors, find A B .

  • A 5 9 i j
  • B 9 + 5 i j
  • C 1 5 i j
  • D + 1 5 i j
  • E 1 5 + i j

Q14:

Given that A i j = 5 6 and B i j = 4 6 , where i and j are two perpendicular unit vectors, find | 2 2 | A B .

  • A2
  • B 2 i
  • C4
  • D 2
  • E 9 1 2 i j

Q15:

Given that A = 3 , 5 , B A and | | = 4 3 4 B , find B .

  • A 8 , 1 6
  • B 3 , 5
  • C 1 2 , 2 0
  • D 1 6 , 2 4

Q16:

Shown on the grid of unit squares are the vectors u v , , and u v + .

What are the components of u ?

  • A 2 , 1
  • B 2 , 4
  • C 2 , 1
  • D 2 , 2
  • E 2 , 2

What are the components of v ?

  • A 3 , 4
  • B 3 , 4
  • C 2 , 4
  • D 3 , 4
  • E 3 , 4

What are the components of u v + ?

  • A 1 , 3
  • B 1 , 3
  • C 1 , 3
  • D 1 , 4
  • E 1 , 3

Q17:

If A = 6 , 4 , 7 , and B = 5 , 6 , 4 , determine A B + .

  • A 2 , 1 1 , 1 1
  • B 1 1 , 2 , 1 1
  • C 1 , 0 , 3
  • D 1 , 1 0 , 3

Q18:

A woman started walking from home and walked 4 miles east, 7 miles southeast, 6 miles south, 5 miles southwest, and 3 miles east. How far did she walk in total? If she walked in a straight line back home, how far would she have to walk? Give your answer correct to three decimal places if necessary.

  • A 15 miles, 16.752 miles
  • B25 miles, 16.752 miles
  • C 15 miles, 21.204 miles
  • D 9 miles, 12.727 miles
  • E 25 miles, 21.204 miles

Q19:

Fill in the blank: If v is a vector in a plane, then the vector 2 v .

  • Amakes an angle of 𝜋 4 with v
  • Bmakes an angle of 0 with v and is twice as long
  • Cmakes an angle of 𝜋 with v and is twice as long
  • Dis perpendicular to v

Q20:

Let z be the zero vector. What is z u + equal to for any vector u ?

  • A u
  • B z

Q21:

Is it always true that 𝐴 𝐵 + 𝐶 𝐷 = 𝐴 𝐷 ?

  • Ayes
  • Bno

Q22:

Is it always true that 𝐴 𝐵 + 𝐵 𝐶 = 𝐴 𝐶 ?

  • ANo
  • BYes

Q23:

Does the vector sum 1 , 2 + 2 , 3 , 1 have a solution?

  • Ayes
  • Bno

Q24:

Let z be the zero vector. What is u z + equal to for any vector u ?

  • A u
  • B z

Q25:

Given that ( 3 , 𝑦 ) + 𝑥 ( 3 , 5 ) ( 0 , 7 ) = 0 , find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 1 , 𝑦 = 2
  • B 𝑥 = 1 , 𝑦 = 2
  • C 𝑥 = 1 , 𝑦 = 1 2
  • D 𝑥 = 1 , 𝑦 = 1 2

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