Angle between vectors (HSC SSCE Mathematics Extension 2): Flashcards
📚Flashcards
Practise the cards
10 cards from this deck
ShowHide
Practise the cards
10 cards from this deck
What is a vector in 3D space?
What is a vector in 3D space?
A vector has size and direction, shown as v = (x, y, z).
How is the angle between vectors defined?
How is the angle between vectors defined?
It's the smallest turn needed from one vector to another.
What is the dot product of vectors?
What is the dot product of vectors?
a · b = ax · bx + ay · by + az · bz.
How do you calculate the magnitude of a vector?
How do you calculate the magnitude of a vector?
|v| = √(x² + y² + z²).
What formula finds the cosine of the angle?
What formula finds the cosine of the angle?
cos(θ) = (u · v) / (|u||v|).
What indicates perpendicular vectors?
What indicates perpendicular vectors?
u · v = 0, θ = 90°.
What indicates parallel vectors?
What indicates parallel vectors?
u · v = |u||v|, θ = 0°.
What is the first step to find the angle between vectors?
What is the first step to find the angle between vectors?
Calculate the dot product u · v.
What values of θ make cos(θ) = 0 in degrees?
What values of θ make cos(θ) = 0 in degrees?
θ = 90° + k*180°, where k is any integer
Why are vector angles important?
Why are vector angles important?
They help in understanding spatial relationships.