Answer:
The angle between vector and
is approximately
radians, which is equivalent to approximately
.
Step-by-step explanation:
The angle between two vectors can be found from the ratio between:
- their dot products, and
- the product of their lengths.
To be precise, if denotes the angle between
and
(assume that
or equivalently
,) then:
.
The first component of is
and the first component of
is also
The second component of is
while the second component of
is
. The product of these two second components is
.
The dot product of and
will thus be:
.
Apply the Pythagorean Theorem to both and
:
.
.
Let represent the angle between
and
. Apply the formula
to find the cosine of this angle:
.
Since is the angle between two vectors, its value should be between
and
(
and
.) That is:
and
. Apply the arccosine function (the inverse of the cosine function) to find the value of
:
.