20. Vectors

Question 1

Vector quantities always have…

Answer 1

a magnitude or norm (length of arrow) and direction (angle arrow makes with axes).

Question 2

Resultant of U (u₁, u₂) and V (v₁, v₂)

Answer 2

U + V = (u₁ + v₁, u₂ + v₂)

Question 3

Vector Addition and Subtraction

a ± b

Answer 3

Addition: head to tail

Subtraction: flip b, then head to tail

Question 4

Vector components

V (x, y)

Answer 4

v = xi + yj

i = (1,0) and j = (0,1)

Question 5

Unit Vector

parallel to u

Answer 5

û = u / ||u||

u = non-zero vector (a, b)

||u|| = √(a² + b²) = norm

Question 6

Dot product of

V (v₁, v₂) and U (u₁, u₂)

Answer 6

V • U = v₁u₁ + v₂u₂

Question 7

Two vector are perpendicular iff…

Answer 7

V • U = 0