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 $pi/2$

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