if vectors a+2b and 5a-4b are perpendicular to each other and a and b are unit vectors. Find the angle between a and b.

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  1. Let θ be the angle between a and b. We know that cosθ = (a∙b) / (|a||b|). Since a and b are unit vectors, |a|=|b|=1. Therefore we need to find a∙b.

    a+2b and 5a-4b are perpendicular, so


    Multiply this out to obtain

    5a∙a + 6a∙b - 8b∙b = 0

    which results in

    6a∙b = 8b∙b - 5a∙a

    Since a and b are unit vectors,

    6a∙b = 8-5 = 3

    Therefore, cos θ = 3/6. θ=π/3

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  3. Good!

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  4. Good

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  5. If two vectors are perpendicular their dot product will equal zero.

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