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:

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

$G_y = -3$