Worksheet: Vector Addition

In this worksheet, we will practice adding two or more vectors in two dimensions, using both graphical and algebraic methods.

Q1:

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

  • AP
  • BS
  • CT
  • DR
  • EQ

Q2:

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

  • AQ
  • BP
  • CT
  • DS
  • ER

Q3:

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

  • AP
  • BT
  • CS
  • DQ
  • ER

Q4:

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

  • AQ
  • BT
  • CS
  • DP
  • ER

Q5:

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

  • AR
  • BS
  • CT
  • DP
  • EQ

Q6:

The diagram shows two vectors, A and B. The grid squares in the diagram have a side length of 1. What is AB+ in component form?

  • A1+2ij
  • B12ij
  • C8+5ij
  • D21ij
  • E58ij

Q7:

Consider the three vectors: A, B, and C. Aij=2+7, Bij=4+8, and Cij=69. Which of the vectors shown in the diagram is equal to ABC++? The grid squares in the diagram have a side length of 1.

  • AR
  • BQ
  • CS
  • DP
  • ET

Q8:

The diagram shows two vectors: A and B. The grid squares in the diagram have a side length of 1. What is AB+ in component form?

  • A7+5ij
  • B5+7ij
  • C1+3ij
  • D1+4ij
  • E3+4ij

Q9:

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

  • AS
  • BR
  • CT
  • DQ
  • EP

Q10:

Consider two vectors A and B. Aij=2+3 and Bij=7+5. Calculate AB+.

  • A5+2ij
  • B2+5ij
  • C5+12ij
  • D8+9ij
  • E9+8ij

Q11:

Which of the vectors P, Q, R, S, and T shown in the diagram is equal to ABC++?

  • AP
  • BS
  • CT
  • DR
  • EQ

Q12:

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

  • AS
  • BR
  • CQ
  • DP
  • ET

Q13:

Which of the vectors P, Q, R, S, and T shown in the diagram is equal to ABC++?

  • AQ
  • BR
  • CP
  • DT
  • ES

Q14:

The diagram shows four vectors: A, B, C, and D. The grid squares in the diagram have a side length of 1. What is ABCD+++ in component form?

  • A56ij
  • B3+9ij
  • C4ij
  • D2+3ij
  • E1+7ij

Q15:

The diagram shows two vectors, A and B. The grid squares in the diagram have a side length of 1. What is AB+ in component form?

  • A53ij
  • B3+5ij
  • C35ij
  • D7+3ij
  • E73ij

Q16:

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

  • AT
  • BQ
  • CP
  • DS
  • ER

Q17:

Consider two vectors: A and B. Aij=5+1 and Bij=2+4. Which of the vectors shown in the diagram is equal to AB+? The grid squares in the diagram have a side length of 1.

  • AT
  • BQ
  • CS
  • DP
  • ER

Q18:

The diagram shows three vectors: A, B, and C. The grid squares in the diagram have a side length of 1. What is ABC++ in component form?

  • A3+7ij
  • B2+1ij
  • C2+13ij
  • D74ij
  • E2+1ij

Q19:

Which three of the vectors shown in the diagram produce a vector with a magnitude of zero when added together?

  • AQ, R, and S
  • BP, R, and T
  • CP, R, and S
  • DQ, R, and T
  • ES, R, and T

Q20:

The diagram shows two vectors: A and B. The grid squares in the diagram have a side length of 1. What is AB+ in component form?

  • A7i
  • B10+3ij
  • C7j
  • D103ij
  • E7j

Q21:

Consider two vectors: A and B. Aij=77 and Bij=62. Calculate AB+.

  • A51ij
  • B139ij
  • C15ij
  • D13+9ij
  • E1+5ij

Q22:

Consider two vectors: A and B. Aij=33 and Bij=4+9. Calculate AB+.

  • A1+6ij
  • B97ij
  • C61ij
  • D16ij
  • E79ij

Q23:

Two forces act on an object: Fij=20+50NN and Fij=30+10NN. What is the total force acting on the object in component form?

  • A5040NNij
  • B10+60NNij
  • C50+40NNij
  • D10+60NNij
  • E6010NNij

Q24:

Two perpendicular forces, F and F, act on an object, as shown in the figure below. Which of the following correctly represents the relation between the magnitude of the resultant force, F, and the magnitudes of the two forces, 𝐹 and 𝐹?

  • A𝐹=𝐹+𝐹
  • B𝐹<𝐹+𝐹
  • C𝐹=𝐹𝐹
  • D𝐹>𝐹+𝐹

Q25:

The following figure shows two vectors of the same type, A and B. If CAB=+, which of the following represents vector C?

  • A
  • B
  • C
  • D

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