If #A = <3 ,3 ,-7 >#, #B = <5 ,8 ,-4 ># and #C=A-B#, what is the angle between A and C?

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Answer 1 · 2016-10-15T19:26:56

This is a special case of the dot-product; we know, without any further computation, that the angle #theta# between the two vectors is #pi/2#

Given:
#barA = <3,3,-7>#,
#barB = <5,8,-4>#,
#barC = barA - barB#

Subtract the components of #barB# from #barA#:

#barC = <(3 - 5), (3 - 8),(-7- -4)>#

#barC = <-2, -5,-3>#

Compute #barA*barC# by multiplying the respective components:

#barA*barC = (3)(-2) + (3)(-5) + (-7)(-3)#

#barA*barC = 0#

This is a special case of the dot-product; we know, without any further computation, that the angle #theta# between the two vectors is #pi/2#