Determine the value of a+b if |3a| = 24 cm, |2b| = 10 cm and |3a-2b| = 20

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asked by Joe
  1. I think something is wrong with your exercise, there is no a and b that match |3a| = 24 cm, |2b| = 10 that can get |3a-2b| = 20 .

    Check image.

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    posted by Arnau EC
  2. This question was given to the class for a test and I have no idea how to do it.

    We were given a similar question

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    posted by Joe
  3. let's suppose a lies along the x-axis, and that 3a-2b makes an angle of θ with a. Then
    |-2b|^2 = |3a|^2 + |3a-2b|^2 - 2*|3a|*|3a-2b|*cosθ
    100 = 576+400-2*24*20cosθ
    Then |-2b| makes an angle of 125.1° with |3a|
    The components of -2b are thus (-5.75,8.18)
    So, b=(2.87,-4.09) and a=(8,0)
    and a+b = (10.87,-4.09)

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    posted by Steve

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