Worksheet: Vector Subtraction

In this worksheet, we will practice subtracting one vector from another in two dimensions, using both graphical and algebraic methods.

Q1:

The diagram shows seven vectors: A, B, P, Q, R, S, and T.

Which of the vectors is equal to AB?

  • AR
  • BQ
  • CT
  • DP
  • ES

Which of the vectors is equal to BA?

  • AP
  • BT
  • CR
  • DS
  • EQ

Q2:

The diagram shows three vectors: A, B, and C. Which of the following expressions gives C in terms of A and B?

  • ACBA=2
  • BCAB=+
  • CCAB=2
  • DCBA=
  • ECAB=

Q3:

Which of the vectors, P, Q, R, S, or T, shown in the diagram is equal to AB?

  • AT
  • BP
  • CQ
  • DR
  • ES

Q4:

Consider the two vectors A and B. Aij=49 and Bij=112. Which of the five vectors shown in the diagram is equal to AB?

  • AR
  • BT
  • CP
  • DQ
  • ES

Q5:

Which of the vectors, P, Q, R, S, or T, shown in the diagram is equal to AB?

  • AT
  • BQ
  • CR
  • DP
  • ES

Q6:

The diagram shows two vectors: A and B. Work out AB in component form.

  • A7+3ij
  • B1210ij
  • C12+10ij
  • D73ij
  • Eij+7

Q7:

Which of the vectors, P, Q, R, S, or T, shown in the diagram is equal to AB?

  • AQ
  • BR
  • CS
  • DT
  • EP

Q8:

Consider the two vectors A and B. Aij=28 and Bij=39. Which of the five vectors shown in the diagram is equal to AB?

  • AQ
  • BR
  • CP
  • DT
  • ES

Q9:

The diagram shows three vectors: A, B, and C. Which of the following expressions gives C in terms of A and B?

  • ACAB=
  • BCAB=2
  • CCAB=+
  • DCBA=
  • ECBA=2

Q10:

Consider two vectors A and B, where Aij=42 and Bij=89. Calculate AB.

  • A1211ij
  • B8+6ij
  • C57ij
  • D4+7ij
  • E12+11ij

Q11:

Consider two vectors A and B, where Aij=84 and Bij=2+5. Calculate AB.

  • A61ij
  • B6+1ij
  • C3+9ij
  • D109ij
  • E22ij

Q12:

Which of the vectors, P, Q, R, S, or T, shown in the diagram is equal to AB?

  • AR
  • BS
  • CP
  • DQ
  • ET

Q13:

Consider the two vectors A and B, where Aij=8+10 and Bij=3+2. Calculate AB.

  • A1112ij
  • B68ij
  • C11+12ij
  • D3+7ij
  • E5+8ij

Q14:

The diagram shows two vectors: A and B. Work out AB in component form.

  • A4+5ij
  • B45ij
  • C8+3ij
  • D83ij
  • E83ij

Q15:

The diagram shows four vectors: A, B, P, and Q.

Which of the vectors P and Q is equal to AB?

  • AP
  • BQ

Which of the vectors P and Q is equal to BA?

  • AQ
  • BP

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