   Chapter 11, Problem 21RE

Chapter
Section
Textbook Problem

# Finding the Angle Between Two Vectors In Exercises 23 and 24, find the angle θ between the vectors (a) in radians and (b) in degrees. u = 5 [ cos ( 3 π / 4 ) i + sin ( 3 π / 4 ) j ] v = 2 [ cos ( 2 π / 3 ) i + sin ( 2 π / 3 ) j ]

(a)

To determine

To calculate: For given the vectors:

u=5[cos3π4i+sin3π4j] and v=2[cos2π3i+sin2π3j]

Find the angle θ between the vectors in radians.

Explanation

Given: The vectors are:

u=5[cos3π4i+sin3π4j] and v=2[cos2π3i+sin2π3j]

Formula used: If θ is the angle between two nonzero vectors u and v. Then,

cosθ=uvuv ;(0θπ)

Calculation:

Component value of u is 52,52.

Given is

u=5[cos3π4i+sin3π4j]=5cos3π4i+5sin3π4j=5(12)i+5(12)j

And

v=2[cos2π3i+sin2π3j]=2(12)i+2(32)j=i+3j

Component value of v is 1,3

(b)

To determine

To calculate: For the vectors u=5[cos3π4i+sin3π4j] and

v=2[cos2π3i+sin2π3j] find The angle θ between them in degree.

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