We will see that for the given vectors:
- a) v.w = -5
- b) The angle between the vectors is 116.57°
How to find the dot product?
Remember that the dot product between two vectors:
a = (x₁, y₁) and b = (x₂, y₂) the dot product is:
a.b = x₁*x₂ + y₁*y₂ = |a|*|b|*cos(θ).
a) We have:
v = (3,-4) and w = (1,2)
The dot product will give:
v.w = 3*1 + (-4)*2 = 3 - 8 = -5
b) We will have:
|v|*|w|*cos(θ) = -5
Where:
- |v| = √(3^2 + (-4)^2) = 5
- |w| = √(1^2 + 2^2) = √5
Then we have:
5*√5*cos(θ) = -5
cos(θ) = -1/√5
θ = Acos(-1/√5) = 116.57°
The angle between the two vectors is 116.57°.
If you want to learn more about vectors, you can read:
https://brainly.com/question/3184914
