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

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SUMMARY

The angle between two vectors can be determined using their dot product, as illustrated in the discussion. Given two vectors with lengths of 23 units and 12 units, and a scalar product of 113, the angle is calculated using the formula A·B = ABcos(θ). The calculation shows that cos(θ) equals 113/276, resulting in an angle θ of approximately 65.8 degrees, which can be rounded to 66 degrees.

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StephenDoty
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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

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