angle between the vectors

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• March 25th 2009, 06:09 PM
oceanmd
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.
• March 25th 2009, 06:20 PM
skeeter
Quote:

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.
• March 25th 2009, 06:27 PM
oceanmd
Thank you very much