CALCULUS!!!!!

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Given the vectors a = (1, 3, 4) and b = (4, 5, -4), what is the angle between the two given vectors to the nearest degree?

  • CALCULUS!!!!! -

    Calculate the cross product using the matrix determinant rule. That will tell you the sine of the angle.

    The magnitudes of the two vectors are
    sqrt(1+9+16) = 5.099 and sqrt(16 + 25 + 16) = 7.550

    The cross product is
    |i j k |
    |1 3 4 |
    |4 5 -4 |
    = -24 i + 20 j -7 k
    The magnitude of the cross product is
    sqrt (576 + 400 + 49) = 32.015

    sin theta = 32.015 /[(5.099)(7.550)]
    = 0.8316
    theta = 56.3 degrees

  • CALCULUS!!!!! -

    wow, thanks so much :) it really helped.

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