Two vectors with magnitudes of 6 and 9 have a dot product equal to –27. Find the angle between the vectors.

120°

Step-by-step explanation:

From the question,

The expression for the dot product of two vector is given as

a.b = abcosθ Equation 1

make θ the subject of the equation

θ =cos⁻¹ (a.b/ab) Equation 2

Where θ = angle between the vector.

Given: a.b = -27, a = 6, b = 9

Substitute these values into equation 2

θ = cos⁻¹[-27/(6×9)]

θ = cos⁻¹(-27/54)

θ = cos⁻¹(-0.5)

θ = 120°.

Hence the angle between the vector is 120°

2

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