sejam os vetores u=(x,3) e v (x+2,-5) a) u e v sejam colineares b)u e v sejam ortogonais

a) u = (x,3) e v = (x+2,-5) colineares:

-> x/(x+2) = 3/(-5)

-> x/3 = -(x+2)/5

-> x/3 = - x/5 - 2/5

-> x/3 + x/5 = - 2/5 (*15)

-> 5x + 3x = - 6

-> 8x = - 6

-> x = - 3/4

b) u = (x,3) e v = (x+2,-5) ortogonais:

-> u.v = 0

-> (x,3)(x+2,-5) = 0

-> x(x+2) - 3*5 = 0

-> x^2 + 2x - 15 = 0

-> (x + 5)(x - 3) = 0

-> x1 = -5, x2 = 3

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