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Find the angle between the given vectors to the nearest degree.

a.
110.7
c.
108.4
b.
71.6
d.
112.5

Find the angle between the given vectors to the nearest degree. a. 110.7 c. 108.4 b-example-1
User Shadam
by
7.4k points

1 Answer

3 votes

Given:

Given that the two vectors are u = (7,-4) and v = (1,5)

We need to determine the angle between these two vectors.

Dot product of u and v:

The dot product of u and v is given by


u \cdot v=(7 * 1)+(-4 * 5)


=7-20


u \cdot v=-13

Magnitude of u:

The magnitude of u is given by


\| u \|=√((7)^2+(-4)^2)


\| u \|=√(49+16)


\| u \|=√(65)

Magnitude of v:

The magnitude of v is given by


\| v \|=√((1)^2+(5)^2)


\| v \|=√(1+25)


\| v \|=√(26)

Angle between the two vectors:

The angle between the two vectors can be determined using the formula,


cos \ \theta=(u \cdot v)/(\| u \| \| v \|)

Substituting the values, we get;


cos \ \theta=(-13)/(√(65) √(26) )


cos \ \theta=(-13)/(41.11 )


cos \ \theta=-0.316


\theta=cos ^(-1)(-0.316)


\theta=108.4^(\circ)

Thus, the angle between the two vectors is 108.4°

User Touti
by
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