Question #ded02

Question

237 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-15T17:53:09

The direction cosines of a vector, #vecv#, are:

#alpha = (vecv*hati)/(|vecv|)#

#beta = (vecv*hatj)/(|vecv|)#

#gamma = (vecv*hatk)/(|vecv|)#

Compute the magnitude of #vecv#:

#|vecv| = sqrt(3^2+ (-4)^2+5^2)#

#|vecv| = 5sqrt2#

#alpha = ((3hati-4hatj+5hatk)*hati)/(5sqrt2)#

#alpha = 3sqrt2/10#

Similarly

#beta = -4sqrt2/10 = -2sqrt2/5#

and

#gamma = 5sqrt2/10 = sqrt2/2#

These are the same as the coordinates of the head of the unit vector of #vecv# with the tail placed at the origin:

#hatv = (3sqrt2/10, -2sqrt2/5, sqrt2/2)#