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Worksheet: Geometrical Interpretation of the Vector Product

Q1:

Find the area of a triangle 𝐴 𝐡 𝐢 , where 𝐴 ( βˆ’ 8 , βˆ’ 9 ) , 𝐡 ( βˆ’ 7 , βˆ’ 8 ) , and 𝐢 ( 9 , βˆ’ 2 ) .

Q2:

Find the area of a triangle 𝐴 𝐡 𝐢 , where 𝐴 ( 0 , 5 ) , 𝐡 ( 7 , βˆ’ 9 ) , and 𝐢 ( βˆ’ 1 , 0 ) .

Q3:

Find the area of a triangle 𝐴 𝐡 𝐢 , where 𝐴 ( 9 , βˆ’ 3 ) , 𝐡 ( βˆ’ 3 , βˆ’ 2 ) , and 𝐢 ( βˆ’ 9 , 2 ) .

Q4:

Find the area of a triangle 𝐴 𝐡 𝐢 , where 𝐴 ( 1 , 4 ) , 𝐡 ( βˆ’ 7 , 6 ) , and 𝐢 ( βˆ’ 9 , βˆ’ 5 ) .

Q5:

Assuming that form a right-hand system; , , and and form two adjacent sides of a triangle, find the product of into and the area of the triangle drawn.

  • A , area square units
  • B , area square units
  • C , area square units
  • D , area square units
  • E , area square units

Q6:

𝐴 𝐡 𝐢 𝐷 is a rhombus, in which the coordinates of the points 𝐴 and 𝐡 are ( 5 , βˆ’ 9 ) and ( βˆ’ 1 0 , 1 2 ) , respectively. Use vectors to determine its perimeter.

  • A666 length units
  • B 3 √ 7 4 length units
  • C 6 √ 7 4 length units
  • D 1 2 √ 7 4 length units

Q7:

If is a triangle of area 248.5 cm2, find the value of .

Q8:

Rhombus 𝐴 𝐡 𝐢 𝐷 has vertices 𝐴 ( βˆ’ 4 , 6 ) , 𝐡 ( 9 , 2 ) , 𝐢 ( βˆ’ 2 , 1 0 ) , and 𝐷 ( βˆ’ 1 5 , 1 4 ) . Use vectors to determine its area.

Q9:

Rhombus 𝐴 𝐡 𝐢 𝐷 has vertices 𝐴 ( 7 , βˆ’ 6 ) , 𝐡 ( 0 , βˆ’ 2 ) , 𝐢 ( βˆ’ 1 , 6 ) , and 𝐷 ( 6 , 2 ) . Use vectors to determine its area.

Q10:

Rhombus 𝐴 𝐡 𝐢 𝐷 has vertices 𝐴 ( 5 , 6 ) , 𝐡 ( βˆ’ 5 , 1 ) , 𝐢 ( βˆ’ 3 , 1 2 ) , and 𝐷 ( 7 , 1 7 ) . Use vectors to determine its area.

Q11:

Rhombus 𝐴 𝐡 𝐢 𝐷 has vertices 𝐴 ( 6 , 1 0 ) , 𝐡 ( 2 , βˆ’ 7 ) , 𝐢 ( βˆ’ 5 , 9 ) , and 𝐷 ( βˆ’ 1 , 2 6 ) . Use vectors to determine its area.

Q12:

Given that 𝐷 = ( 0 , βˆ’ 2 , βˆ’ 8 ) , 𝐸 = ( 6 , 4 , 6 ) , and 𝐹 = ( βˆ’ 4 , βˆ’ 9 , βˆ’ 2 ) , determine the area of the triangle 𝐷 𝐸 𝐹 approximated to the nearest hundredth.

Q13:

Given that 𝐷 = ( βˆ’ 2 , 0 , βˆ’ 2 ) , 𝐸 = ( βˆ’ 3 , βˆ’ 9 , 5 ) , and 𝐹 = ( βˆ’ 5 , βˆ’ 1 , βˆ’ 6 ) , determine the area of the triangle 𝐷 𝐸 𝐹 approximated to the nearest hundredth.

Q14:

Triangle 𝐴 𝐡 𝐢 has vertices 𝐴 ( 5 , βˆ’ 4 ) , 𝐡 ( βˆ’ 1 , βˆ’ 5 ) , and 𝐢 ( βˆ’ 3 , 2 ) . Use vectors to determine its area.

Q15:

Suppose that and fix two sides of a triangle. What is the area of this triangle, to the nearest hundredth?

Q16:

Suppose that and fix two sides of a triangle. What is the area of this triangle, to the nearest hundredth?

Q17:

Suppose that and fix two sides of a triangle. What is the area of this triangle, to the nearest hundredth?