# Math Help - angle between the vectors

1. ## angle between the vectors

Please check my work. Thank you.
Find the dot product of the following vectors. Find the angle between the vectors.
v=3i+2j, w=-4i-5j
Dot product v x w=-12-10=-22
cos of angle = -22/sq. root of 13 x sq. root of 41=-0.9529
the angle = 17.64 degrees.

Please tell me where I made a mistake, because when I graph the vectors, the angle looks like it is about 100 degrees.

Thank you very much.

2. Originally Posted by oceanmd
Please check my work. Thank you.
Find the dot product of the following vectors. Find the angle between the vectors.
v=3i+2j, w=-4i-5j
Dot product v x w=-12-10=-22
cos of angle = -22/sq. root of 13 x sq. root of 41=-0.9529
the angle = 17.64 degrees.

Please tell me where I made a mistake, because when I graph the vectors, the angle looks like it is about 100 degrees.

Thank you very much.
a bit larger than 100 degrees, but it is obtuse ...

$\theta = \arccos(-0.9529) = 162.3^{\circ}$

inverse cosine of a negative value yields a quad II angle.

3. Thank you very much