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Chapter 3: Q39P (page 59)

Vector A鈫�has a magnitude of6.00units, vectorB鈫�has magnitude of7.00units, andA鈫�.B鈫�has a value of14.0What is the angle between the directions of A鈫�and B鈫�?

Short Answer

Expert verified

The angle 胃between A鈫�and B鈫�is 70.5掳.

Step by step solution

01

Vector operations

The dot product of the vectors is equal to the product of the magnitude of the vectors and the cosine of the angle between them. Using this definition, find the value of the angle between the two vectors when the magnitude and dot product are given. The formula for the dot product is,

a鈫�.b鈫�=a.b.c0s胃 (i)

The magnitude of the vector A鈫�is 6.00units. The magnitude of vector B鈫�is7.00units. The dot product of two vector is equal to14.0units

02

Finding the direction between two vectors

Substitute the given values in equation (i)

a鈫�.b鈫�=a.b.cos胃14.0=6.00脳7.00脳cos胃14.0=42脳cos胃cos胃=14.042胃=cos-114.042=70.5掳

Therefore, the angle between the two vectors is 70.5掳.

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