Question

Find the angle between u=-4i+3j and w=-5i-7j

Answer 1

can you find the angle for the individual vector????

Answer 2

think about dot product

Answer 3

add like times -4j+3j is u=-j and w=-12j so it has to be between -1j and -12j

Answer 4

steps:
first find the angle of U
then find the angle of W
subtract the smaller angle from the larger, the result is the angle between these vectors.

Answer 5

Since dot product is also given as...
\[\Large \vec u \cdot \vec w = |\vec u||\vec w|\cos(\theta)\]
Then it follows that
\[\Large \cos(\theta) = \frac{\vec u \cdot \vec w}{|\vec u||\vec w|}\]