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Lesson: The Angle between Two Vectors in the Coordinate Plane

Sample Question Videos

Worksheet • 25 Questions • 3 Videos

Q1:

.

  • A
  • B
  • C
  • D
  • E

Q2:

If and satisfy , how are the two vectors related?

  • Aparallel
  • Bperpendicular

Q3:

If and are two perpendicular vectors, then .

Q4:

If and , where the size of the angle between and is , find to the nearest hundredth.

  • A
  • B
  • C85.00
  • D

Q5:

If and , where the size of the angle between and is , find to the nearest hundredth.

  • A
    1 170.50
  • B
  • C
  • D663.50

Q6:

If and , where the size of the angle between and is , find to the nearest hundredth.

  • A
  • B
  • C
  • D251.82

Q7:

Suppose 𝐴 𝐡 𝐢 𝐷 is a square of side 47. Determine οƒ  𝐴 𝐡 β‹… οƒ  𝐴 𝐢 .

Q8:

Suppose square 𝐴 𝐡 𝐢 𝐷 of side 32.6. Determine οƒ  𝐴 𝐷 β‹… οƒ  𝐴 𝐢 .

Q9:

Suppose a rectangle 𝐴 𝐡 𝐢 𝐷 with 𝐴 𝐡 = 3 2 and 𝐡 𝐢 = 1 1 . Determine οƒ  𝐴 𝐢 β‹… οƒ  𝐡 𝐷 .

Q10:

In rectangle 𝐴 𝐡 𝐢 𝐷 , we have 𝐴 𝐡 = 1 5 and 𝐡 𝐢 = 1 1 . Determine ο€Ί οƒŸ 𝐡 𝐢  β‹… ο€Ί 5 οƒ  𝐷 𝐡  to the nearest hundredth.

Q11:

In a rectangle 𝐴 𝐡 𝐢 𝐷 , 𝐴 𝐡 = 7 . 7 and 𝐡 𝐢 = 3 . 8 . Determine ο€Ί 5 οƒ  𝐴 𝐡  β‹… ο€Ί οƒ  𝐴 𝐢  .

Q12:

If 𝐴 𝐡 𝐢 𝐷 𝐸 𝐹 is a regular hexagon whose side is 7.1, find ο€Ί οƒ  𝐢 𝐴 + οƒ  𝐴 𝐹  β‹… οƒ  𝐴 𝐷 .

Q13:

If 𝐴 𝐡 𝐢 𝐷 𝐸 𝐹 is a regular hexagon whose side is 17.2, find ο€Ί οƒ  𝐢 𝐴 + οƒ  𝐴 𝐹  β‹… οƒ  𝐴 𝐷 .

Q14:

If 𝐴 𝐡 𝐢 𝐷 𝐸 𝐹 is a regular hexagon whose side is 9.6, find ο€Ί οƒ  𝐴 𝐡 βˆ’ οƒŸ 𝐸 𝐹  β‹… οƒ  𝐴 𝐷 .

Q15:

If 𝐴 𝐡 𝐢 𝐷 𝐸 𝐹 is a regular hexagon whose side is 32.3, find ο€Ί οƒ  𝐴 𝐡 βˆ’ οƒŸ 𝐸 𝐹  β‹… οƒ  𝐴 𝐷 .

Q16:

If 𝐴 𝐡 𝐢 𝐷 𝐸 𝐹 is a regular hexagon whose side is 32.6, find ο€Ί οƒ  𝐴 𝐡 βˆ’ οƒŸ 𝐸 𝐹  β‹… οƒ  𝐴 𝐷 .

Q17:

Triangle 𝐴 𝐡 𝐢 has a right angle at 𝐡 . Given 𝐴 𝐡 = 2 0 , 𝐡 𝐢 = 5 , and that 𝐷 is the midpoint of 𝐴 𝐢 . Determine οƒ  𝐷 𝐡 β‹… ο€Ό 7 5 οƒŸ 𝐡 𝐢  to the nearest hundredth.

Q18:

Triangle 𝐴 𝐡 𝐢 has a right angle at 𝐡 . Given 𝐴 𝐡 = 3 8 . 6 , 𝐡 𝐢 = 3 6 . 4 , and that 𝐷 is the midpoint of 𝐴 𝐢 , determine οƒ  𝐡 𝐴 β‹… οƒ  𝐡 𝐷 to the nearest hundredth.

Q19:

Triangle 𝐴 𝐡 𝐢 has a right angle at 𝐡 . Given 𝐴 𝐡 = 3 1 . 2 and 𝐡 𝐢 = 2 0 . 4 , determine οƒ  𝐴 𝐡 β‹… οƒ  𝐴 𝐢 .

Q20:

If and , find all the possible values of that make the size of the angle between the two vectors .

  • A or
  • B or
  • C or
  • D or

Q21:

Let and Find the angle between A and B giving your answer to two decimal places.

Q22:

Given that , and , determine the angle between the two vectors rounded to the nearest minute.

  • A
  • B
  • C
  • D

Q23:

If , find the value of in the range .

Q24:

If , , and the size of the angle between and is , calculate .

  • A
  • B
  • C
  • D
  • E80

Q25:

If , find the value of in the range .

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