Worksheet: The Vector Product of Two Vectors

In this worksheet, we will practice calculating the vector product of two vectors using both the components of the vectors and the magnitudes of the two vectors and the angle between them.

Q1:

Consider the two vectors Rij=3+2 and Sij=5+8. Calculate RS×.

  • A1k
  • B1k
  • C14k
  • D34k
  • E14k

Q2:

Two vectors, a and b, have the same length and are perpendicular to each other. The vector product of a and b has a magnitude of 9. What is the length of each vector?

Q3:

The diagram shows two vectors, A and B, in three-dimensional space. Both vectors lie in the 𝑥𝑦-plane. Each of the squares on the grid has a side length of 1. Calculate AB×.

  • A31k
  • B8k
  • C32k
  • D8k
  • E32k

Q4:

The diagram shows two vectors, A and B, in three-dimensional space. Both vectors lie in the 𝑥𝑦-plane. Each of the squares on the grid has a side length of 1. Calculate AB×.

  • A13k
  • B17k
  • C11k
  • D13k
  • E7k

Q5:

The diagram shows two vectors, A and B. Each of the grid squares in the diagram has a side length of 1. Calculate AB×.

  • A32k
  • B28k
  • C4k
  • D32k
  • E28k

Q6:

Work out ji×.

  • Aj
  • Bi
  • Ci
  • Dk
  • Ek

Q7:

The diagram shows a rod r that can rotate around point P. A force F is applied to the end of the rod. Each of the squares of the grid has a side length equal to 1 m and 1 N. The torque on the rod is equal to the vector product of r and F. Calculate the magnitude of the torque on the rod.

Q8:

The diagram shows two vectors, C and D, in three-dimensional space. Both vectors lie in the 𝑥𝑦-plane. Each of the squares of the grid has a side length of 1. Calculate CD×.

  • A11.3k
  • B2.8k
  • C5.7k
  • D11.3k
  • E0k

Q9:

The diagram shows a rod with a length of 1.5 m that can rotate around point P. A force with a magnitude of 12 N is applied to the end of the rod. What is the magnitude of the torque applied to the rod?

Q10:

Consider the two vectors Aij=6+7 and Bij=12+4. Does AB× point in the positive 𝑧-direction or the negative 𝑧-direction?

  • AThepositive-direction𝑧
  • BThenegative-direction𝑧

Q11:

The diagram shows two vectors, A and B. Calculate the magnitude of the vector product of A and B. Give your answer to 2 significant figures.

Q12:

Consider the two vectors Cij=15+7 and Dij=4+9.

Calculate CD×.

  • A3k
  • B163k
  • C107k
  • D123k
  • E107k

Calculate DC×.

  • A107k
  • B163k
  • C107k
  • D3k
  • E123k

Q13:

Complete the following: The diagram shows six vectors, A, P, Q, R, S, and T, in three-dimensional space. All of the vectors lie in the 𝑥𝑦-plane, and all have the same length. The vector product of A and has the greatest magnitude.

  • AS
  • BR
  • CT
  • DQ
  • EP

Q14:

The diagram shows two vectors, A and B, in three-dimensional space. Both vectors lie in the 𝑥𝑦-plane. Each of the squares of the grid has a side length of 1. Calculate AB×.

  • A15k
  • B27k
  • C23k
  • D27k
  • E15k

Q15:

The diagram shows two vectors, A and B. Each of the grid squares in the diagram has a side length of 1. Calculate AB×.

  • A16k
  • B24k
  • C11k
  • D19k
  • E16k

Q16:

The diagram shows two vectors, A and B. Each of the grid squares in the diagram has a side length of 1. Calculate AB×.

  • A11k
  • B7k
  • C7k
  • D17k
  • E17k

Q17:

The diagram shows a rod with a length of 2.2 m that can rotate around point P. A force with a magnitude of 35 N is applied to the end of the rod. What is the magnitude of the torque applied to the rod? Give your answer to 2 significant figures.

Q18:

Work out ij×.

  • Ai
  • Bk
  • Ci
  • Dj
  • Ek

Q19:

The diagram shows two vectors, A and B. The magnitude of the vector product of A and B is 6.8. Calculate the angle between the two vectors, 𝜃. Give your answer to 2 significant figures.

Q20:

Consider the two vectors A and B. A has a length of 4 and B has a length of 13. The angle between them is 78. Calculate the magnitude of AB×. Give your answer to 3 significant figures.

  • A50.9
  • B8.80
  • C245
  • D10.8
  • E16.6

Q21:

The diagram shows two vectors, A and B. Each of the grid squares in the diagram has a side length of 1. Calculate AB×.

  • A1k
  • B18k
  • C18k
  • D6k
  • E6k

Q22:

Consider the two vectors pij=4+5 and qij=2+8. Calculate pq×.

  • A42k
  • B22k
  • C48k
  • D32k
  • E22k

Q23:

The diagram shows two vectors, A and B. Each of the grid squares in the diagram has a side length of 1. Calculate AB×.

  • A20k
  • B16k
  • C20k
  • D16k
  • E9k

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