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5 May, 00:59

Determine whether u and v are orthogonal, parallel, or neither. u =

v=

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  1. 5 May, 02:25
    0
    Take the dot product, if the dot product is zero, they are orthogonal

    the dot product here is 15 (-5) + 45 (12) so the vectors are not orthogonal

    to see if they are parallel, take the dot product again, using the definition

    u dot v = mag u x mag v cos (theta) where mag is the magnitude of the vector and theta is the angle between them

    we know from above that u dot v = 465

    mag u = sqrt[15^2+45^2]=47.43

    mag v = sqrt[5^2+12^2]=13

    so we know:

    cos (theta) = 465 / (47.43x13) = 0.75

    so theta = 41 deg
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