FM - Further Pure 1 - 1) Vectors

Question 1

Formulas for the vector cross product

Answer 1

• a x b = |a||b|sin(θ)n̂
  ( i j k )
  |a₁ a₂ a₃|
  |b₁ b₂ b₃|

Question 2

Formula to find a unit vector

Answer 2

(1/magnitude)·vector

Question 3

Formula for area of a triangle using vectors

Answer 3

½|a x b|

Question 4

Formula for area of a parallelogram using vectors

Answer 4

|a x b|

Question 5

Formula for scalar triple vector product

Answer 5

• a · (b x c)
  |a₁ a₂ a₃|
  |b₁ b₂ b₃|
  |c₁ c₂ c₃|

Question 6

Formula for volume of a parallelepiped using vectors

Answer 6

|a · (b x c)|

Question 7

Formula for volume of a tetrahedron using vectors

Answer 7

1/6·|a · (b x c)|