Find the scalar product of the two vectors A and B. Find the angle between

kuCAu

kuCAu

Answered question

2021-08-18

Find the scalar product of the two vectors A and B.
Find the angle between these two vectors.
A=2.00ı+6.00ȷandB=2.00ı3.00ȷ

Answer & Explanation

coffentw

coffentw

Skilled2021-08-19Added 103 answers

Remember that the scalar product is just what you get when you multiply the like "components" together and then add them up. Hence
AB=(2i+6j)(2i3j)=(2)(2)+(6)(3)=22
To calculate the angle between two vectors, we use the formula
AB=ABcos(θ)
Solving for θ, we get
θ=arccos(ABAB)
We already have A⋅B, so we just need to calculate the lengths of A and B.
A=(2)2+62=210
B=22+(32)=13
Therefore
θ=arccos(222130)2.88rad

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