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.

  • AMij=2+52, ||=412M
  • BMij=522, ||=322M
  • CMij=52+2, ||=322M
  • DMij=522, ||=412M
  • EMij=52+2, ||=412M

Q2:

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

  • A72+92ij
  • B92+72ij
  • C927ij
  • D9+72ij

Q3:

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

  • A210ij
  • B2+10ij
  • C2+10ij
  • D210ij
  • E10+2ij

Q4:

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

  • AZi=52
  • BZij=1952
  • CZij=5219
  • DZij=52+19
  • EZj=19

Q5:

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

  • A2+ij
  • B2ij
  • C22ij
  • Dij+
  • Eij2

Q6:

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

  • A2+ij
  • Bij+2
  • C2j
  • D2i
  • E2+2ij

Q7:

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

  • A2,0
  • B0,2
  • C2,2
  • D1,2
  • E2,1

Q8:

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

  • A7,5
  • B5,7
  • C7,5
  • D5,7
  • E7,5

Q9:

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

  • A2,4
  • B4,2
  • C2,4
  • D2,4
  • E4,2

Q10:

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

  • A35ij
  • B53ij
  • C5+3ij
  • D35ij
  • E3+5ij

Q11:

Find the unit vector in the direction of 𝑃𝑄.

  • A889,589
  • B213,313
  • C213,313
  • D889,589
  • E589,889

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