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the sides of a parallelogram are determined by the vectors m= (2,-3,5) and n= (-1,7,5). determine

a. the larger angle between the diagonals of this parallelogram.
b. the smaller angle between the sides

recall that u•v = |u| |v| cosθ

Did you know?

Did you know that in a parallelogram, the sides can be determined by vectors? For example, if we have vectors m= (2,-3,5) and n= (-1,7,5), we can determine the sides of the parallelogram. Now, let's look at the angles. a. The larger angle between the diagonals of this parallelogram can be found using the dot product formula: cos(theta) = (m•n) / (||m|| ||n||), where theta is the desired angle. By calculating the dot product (m•n) and the magnitudes (||m|| and ||n||), we can find the cosine of the angle. We can then take the inverse cosine to find the angle itself. b. On the other hand, the smaller angle between the sides can be found using the dot product formula as well. By calculating the dot product (m•n) and the magnitudes (||m|| and ||n||), we can find the cosine of the angle. We can then take the inverse cosine to find the angle itself. These calculations allow us to better understand the angles within a parallelogram and how they relate to the given vectors.