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Given vectors u=7i + 3j and v = -4i + 3j, find 5u-4v in terms of unit vectors.

I am just beginning the study of vectors and have this problem. Could someone help? Thanks.

  • PreCalculus -

    handle them just like algebraic expressions
    u=7i + 3j and v = -4i + 3j

    then 5u - 4v
    = 5(7i+3j) - 4(-4i+3j)
    = 35i + 15j + 16i - 12j
    = 51i + 3j

  • PreCalculus -

    Dear Reiny,

    Thank you for helping me. Could you check an answer for me?

    Use a metric ruler and a protractor to find 2 a (vector) - 2 b (vector). Then find the magnitude and amplitude of the resultant.

    Vector a is 4 cm and the angle is 60 degrees. Vector b is 1 centimeter long and the angle is 135 degrees.

    My answer for magnitude was 4 cm with the angle being 31 degrees. Is this correct?

  • PreCalculus -

    vector a = 4 cos 60 i + 4 sin 60 j
    = 2 i + 0.866 j
    vector b = -2.828 i + 2.828 j

    "i" and "j" indicate the components along the x and y axes. It is a commonly used vector notation

    a - b = -0.828 i + 3.694j
    magnitude of a - b = 3.785
    magnitude of 2 (a-b) = 7.571

    Your angle is also wrong

  • PreCalculus -

    Hi drwls--

    I have just begun the study of vectors. I am given the answer in multiple choice--The answer you gave me is 7.571. The choices I have are 8cm;41 degrees; 9cm;38degrees;6cm,36degrees, and 4cm,31 degrees.

    Your answer is closest to 8 cm. Is that the one I should select? Thanks.

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