Find x so that B = 3x i +5j is perpendicular to is perpendicular to A=2i – 6j​

Find x so that B = 3x i +5j is perpendicular to is perpendicular to A=2i – 6j​

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  1. Answer:

    5

    Step-by-step explanation:

    I’m going to call x, x1 because I want to use x as a variable.

    So we have a ray with points (0,0) and (3×1,5) on it. This equation for this ray would be y=5/(3×1)×x.

    We have another ray with points (0,0) and (2,-6). This equation for this ray would be y=-6/2×x or y=-3x.

    We want these two lines’ slopes to be opposite reciprocals. The opposite reciprocal of -3 is 1/3.

    So we want to find x1 such that 5/(3×1)=1/3.

    Cross multiply: 15=3×1

    Divide both sides by 3: 5=x1

    We want x1 to be 5 so that 5/(3×5) and -3 are opposite reciprocals which they are.

    Another way:

    If two vectors are perpendicular, then their dot product is 0.

    The dot product of <3x,5> and <2,-6> is 3x(2)+5(-6).

    Let’s simplify:

    6x-30.

    We want this to be 0.

    6x-30=0

    Add 30 on both sides:

    6x=30

    Divide both sides by 6:

    x=5

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