   Chapter 11.3, Problem 12E

Chapter
Section
Textbook Problem

# Finding the Angle Between Two Vectors In Exercises 11–18, find the angle θ between the vectors (a) in radians and (b) in degrees. u = cos ( π 6 ) i + sin ( π 6 ) j , v = cos ( 3 π 4 ) i + sin ( 3 π 4 ) j

(a)

To determine

To calculate: The angle θ between the vectors u=cosπ6i+sinπ6jandv=cos3π4i+sin3π4j in radians.

Explanation

Given:

The provided vectors are u=cosπ6i+sinπ6jandv=cos3π4i+sin3π4j.

Formula used:

Formula for dot product is given by:

uv=uvcos(θ)cos(θ)=uvuvθ=arccos(uvuv)

Where the vector u=uu and v=vv and θ is the angle between the vectors uand v.

Dot product of the vectors u=u1i+u2jandv=v1i+v2j is uv=u1v1+u2v2

(b)

To determine

To calculate: The angle θ between the vectors u=cosπ6i+sinπ6jandv=cos3π4i+sin3π4j in degrees.

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