Question

sejam u=(2,6,-4), v=(-1,-4,8), e w=(0,-7,5). Encontre
a)u+v-3w
b)||v+w||
c)||v||-||w||
d)(3u+w)-(-3v+u

Answer 1

a) u + v - 3w = (2 - 1 - 3.0, 6 - 4 - 3.(-7), -4 + 8 - 3.5) = (1, 23, -11)

b) ||v + w|| = ||(-1, -4, 8) + (0, -7, 5)|| = ||(-1 + 0, -4 - 7, 8 + 5)|| = ||(-1, -11, 13)|| = √(-1)² + (-11)² + 13² = √1 + 121 + 169 = √291

c) ||v|| - ||w||

||v|| = √(-1)² + (-4)² + 8² = √81 = 9

||w|| = √0² + (-7)² + 5² = √74

||v|| - ||w|| = 9 - √74

d) (3u + w) - (-3v + u)

3u = 3(2, 6, -4) = (6, 18, -12)

(6, 18, -12) + (0, -7, 5) = (6, 11, -7)

-3v = -3(-1, -4, 8) = (3, 12, -24)

(3, 12, -24) + (2, 6, -4) = (5, 18, -28)

(3u + w) - (-3v + u) = (6, 11, -7) - (5, 18, -28) = (1, -7, 21)