Let F = 2i - 6j + 10k and G = i+ Gy j + 5k. If F and G have the same unit vector, what is Gy?

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Answer 1 · 2016-11-19T18:00:11

#G_y = -3#

Given: #barF = 2hati - 6hatj + 10hatk#.

The phrase; "If #barF# and #barG# have the same unit vector" allows us to write the equation:

#barG = k(barF)#

where k is a scalar multiplier.

We can find the value of the multiplier by examining the #hati# components of the two vectors:

#hati = (k)2hati#

#k = 1/2#

This is consistent with the #hatk# component of the two vectors, too:

#5hatk = (1/2)10hatk#

Therefore, we apply the same scalar multiplier to the #hatj# components:

#G_yhatj = (1/2)(-6hatj)#

#G_y = -3#