Scalar product of vectors (HSC SSCE Mathematics Extension 1): Flashcards
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What is the scalar product of vectors?
What is the scalar product of vectors?
A value without direction from vector magnitudes and angle.
How is the scalar product denoted?
How is the scalar product denoted?
It is expressed as α · β for vectors α and β.
What is the formula for scalar product?
What is the formula for scalar product?
α · β = |α| |β| cos θ.
What does the scalar product indicate?
What does the scalar product indicate?
It shows the relationship between vector magnitudes and angle.
What is the component form of scalar product?
What is the component form of scalar product?
α · β = a1b1 + a2b2.
What happens with parallel vectors?
What happens with parallel vectors?
Their scalar product equals the product of their magnitudes.
What is the scalar product of perpendicular vectors?
What is the scalar product of perpendicular vectors?
It is zero when vectors are perpendicular.
How to find the angle between vectors?
How to find the angle between vectors?
Use cos θ = α · β / (|α| |β|).
What does a scalar product of zero indicate?
What does a scalar product of zero indicate?
It indicates that the vectors are orthogonal.
What does the scalar product of a vector with itself yield?
What does the scalar product of a vector with itself yield?
It gives the square of the vector's magnitude.