How Is the Angle Between Two Vectors Determined Using Their Dot Product?

Thread starter StephenDoty
Start date Apr 11, 2008
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Angle Dot Dot product Product

AI Thread Summary

The angle between two vectors can be determined using their dot product formula, A·B = ABcos(theta). Given one vector of length 23 units and another of 12 units, with a scalar product of 113, the calculation proceeds as follows: 113 = 12*23*cos(theta). This simplifies to cos(theta) = 113/276, leading to theta = cos^(-1)(113/276). The resulting angle is approximately 65.8 degrees, which can be rounded to 66 degrees.

Apr 11, 2008

StephenDoty

One vector has a length of 23 units and another a length of 12 units. If the scalar product of these two vectors is 113, what is the angle between the two vectors?

A dot B = ABcos(theta)
113 = 12*23*cos(theta)
113/276= cos(theta)
cos^(-1)113/276 = theta
65.8 degrees or 66 degrees using sig figs = theta

is this right?

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Apr 11, 2008

neu

yes yes

Apr 12, 2008

physixguru

easy.

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