Find two vectors in opposite directions that are orthogonal

Find two vectors in opposite directions that are orthogonal to the vector u. u = 1/4 i - 4/5 j positive x-component positive y-component 4/5i negative x-component, negative y-component -4/5i - 1/4j Use the vectors u = and v = (-7, 7) to find the indicated quantity. 3u - v 3u - v = 87

Solution

u = (1/4)i - (4/5)j

let the vector be ai + bj

then a/4 - 4b/5 = 0

a = 16b/5

let b = 5, a = 16

so two required opposite vectors can be, 16i + 5j and -16i - 5j

2) u = 2i + 5j

v = -7i + 7j

3u.v = 3 x (-14 + 35) = 63