Math

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Find the dot product of the following vectors:

a = (4, 1) b = (-1,4)

a = (7,8) b = (4, -7)

You have to find the angle too.

Can someone please do these?

  • Math -

    4*-1 + 1*4 = 0
    cos angle = 0, so angle is 90 or -90 (240)
    remember algebra 1
    y = m x + b
    the slope of a line perpendicular to that is -1/m
    here we have a slope of 1/4
    and the other slope is 4/-1
    sure enough, perpendicular

    7*4 + 8*-7
    7*(4-8)= -28
    |A|*|B|* cos angle = -28
    sqrt(49+64)*sqrt(16+49)* cos angle = -28
    10.6 * 8.06 *cos angle = -28
    cos angle = -.328
    angle = 109 deg

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