Worksheet: Vectors in Terms of Fundamental Unit Vectors

In this worksheet, we will practice writing vectors in component form using fundamental unit vectors.

Q1:

Given that M=52,2, express the vector M in terms of the unit vectors i and j, and find its norm ||M.

  • A M i j = 2 + 5 2 , | | = 4 1 2 M
  • B M i j = 5 2 2 , | | = 3 2 2 M
  • C M i j = 5 2 + 2 , | | = 3 2 2 M
  • D M i j = 5 2 2 , | | = 4 1 2 M
  • E M i j = 5 2 + 2 , | | = 4 1 2 M

Q2:

Given that Aij=97, where i and j are two perpendicular unit vectors, find 12A.

  • A 7 2 + 9 2 i j
  • B 9 2 + 7 2 i j
  • C 9 2 7 i j
  • D 9 + 7 2 i j

Q3:

The given figure shows a vector in a plane. Express this vector in terms of the unit vectors i and j.

  • A 2 1 0 i j
  • B 2 + 1 0 i j
  • C 2 + 1 0 i j
  • D 2 1 0 i j
  • E 1 0 + 2 i j

Q4:

Express the vector Z=52,19 using the unit vectors i and j.

  • A Z i = 5 2
  • B Z i j = 1 9 5 2
  • C Z i j = 5 2 1 9
  • D Z i j = 5 2 + 1 9
  • E Z j = 1 9

Q5:

Given that A=2,1, express the vector A in terms of the unit vectors i and j.

  • A 2 + i j
  • B 2 i j
  • C 2 2 i j
  • D i j +
  • E i j 2

Q6:

Given that A=0,2, express the vector A in terms of the unit vectors i and j.

  • A 2 + i j
  • B i j + 2
  • C 2 j
  • D 2 i
  • E 2 + 2 i j

Q7:

Given that Ai=2, write the vector A in Cartesian coordinates.

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

Q8:

Given that Aij=57, write the vector A in Cartesian coordinates.

  • A 7 , 5
  • B 5 , 7
  • C 7 , 5
  • D 5 , 7
  • E 7 , 5

Q9:

Given that Aij=2+4, write the vector A in Cartesian coordinates.

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

Q10:

Given that A=3,5, express the vector A in terms of the unit vectors i and j.

  • A 3 5 i j
  • B 5 3 i j
  • C 5 + 3 i j
  • D 3 5 i j
  • E 3 + 5 i j

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