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A vectors who tail is at the origin, and whose head is at (-3, -4, 15)N,...

A vectors who tail is at the origin, and whose head is at (-3, -4, 15)N, what are the directional angles that describe the direction of this vector?

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Homework Answers

Answer #1

A = (0, 0, 0)

B = (-3, -4, 15)

AB = <-3, -4, 15> - <0, 0, 0>

AB = <-3, -4, 15>

Direction angles are given by:

cos = a/sqrt (a^2 + b^2 + c^2)

= arccos [a/sqrt (a^2 + b^2 + c^2)]

cos = b/sqrt (a^2 + b^2 + c^2)

= arccos [b/sqrt (a^2 + b^2 + c^2)]

cos = c/sqrt (a^2 + b^2 + c^2)

= arccos [c/sqrt (a^2 + b^2 + c^2)]

here a = -3, b = -4, and c = 15

So,

= arccos [(-3)/sqrt (9 + 16 + 225)] = 100.93 deg

= arccos [(-4)/sqrt (9 + 16 + 225)] = 104.65 deg

= arccos [(15)/sqrt (9 + 16 + 225)] = 18.43 deg

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