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the position vectors of the point A,B & C respect to O are a=3i-2j+4k, b=i+3j-4k, c=-2i+5j-3k. Find
a)the angle between a+b and a-b
b)lamdar if vector a is perpendicular to b+lamdar k.

  • math -

    How do you define "lambdar" ?

    As for part (a), compute these two vectors:
    a + b = 4i +j +0k
    a - b = 2i -5j +4k

    Their magnitudes are:

    |a+b| = sqrt(16 + 1) = sqrt17
    |a-b| = sqrt(4 +25 + 16) = sqrt45

    (a+b)*(a-b) = 8 -5 = 3
    = (sqrt17) x (sqrt45) cos theta

    cos theta = 3/sqrt765 = 0.108
    theta = 83.8 degrees

    In the above, * denotes a dot product and x denotes normal scalar multiplication

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