To locate the angle θ in between 2 vectors C and also D, we can make use of the adhering to formula:
$$ cos( theta) = frac {vec {C} cdot vec {D}} ~ $$
where $latex vec {C} cdot vec {D} $ is the dot item of $latex vec {C} $ and also $latex vec {D} $, and also|C|and also|D|are the sizes of the vectors.
First, we locate the dot item:
$ latex vec {C} cdot vec {D} = (1 times 0) + (1 times -1) + (0 times 1) = -1$
Now, we locate the sizes:
$ latex|C|= sqrt {1 ^ 2 + 1 ^ 2 + 0 ^ 2} = sqrt {2} $
$ latex|D|= sqrt {0 ^ 2 + (-1 )^ 2 + 1 ^ 2} = sqrt {2} $
Then, we determine cos( θ):
$$ cos( theta) = frac {-1} {sqrt {2} times sqrt {2}} $$
$$ = -frac {1} {2} $$
Finally, we locate the angle θ:
$ latex theta = message {arccos} (- frac {1} {2}) approx 120 ^ {circ} $