FM - Core Pure 1 - 9) Vectors

Question 1

Vector equation of a straight line

Answer 1

r = a + λb

Question 2

Vector equation of a straight line passing through two points

Answer 2

r = a + λ(b-a)

Question 3

Cartesian form of a vector equation of a line

Answer 3

(x-a₁)/b₁ = (y-a₂)/b₂ = (z-a₃)/b₃ = λ

Question 4

Vector equation of a plane

Answer 4

r = a + λb + µc

Question 5

Cartesian form of a vector equation of a plane

Answer 5

ax + by + cz = d → (a b c) is the normal vector to the plane

Question 6

Formula for the scalar (dot) product and information that shows when two vectors are perpendicular and parallel

Answer 6

• a·b = |a||b|cos(θ)
• Perpendicular → a·b = 0
• Parallel → a·b = |a||b| → a·a = |a|²

Question 7

Formula for the scalar (dot) product and information that shows when two vectors are perpendicular and parallel

Answer 7

• a·b = |a||b|cos(θ)
• Perpendicular → a·b = 0
• Parallel → a·b = |a||b| → a·a = |a|²

Question 8

PLANE EQUATION

Answer 8

.

Question 9

ANGLE BETWEEN… X3

Answer 9

→ when both vectors are pointing in the same direction - if they point in opposite directions,