# A parallelogram is determined by the vectors a = (-2,5) and b = (3,2). Determined the angles between the diagonals of the parallelogram?

Using the Law of Cosines

A triangle is formed by half of the lengths of the two diagonals, and either of the lengths of the original vectors.

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To find the angles between the diagonals of the parallelogram determined by the vectors ( \mathbf{a} = (-2, 5) ) and ( \mathbf{b} = (3, 2) ), we first need to find the vectors representing the diagonals.

The diagonals of a parallelogram are formed by the sum and difference of its adjacent sides. Therefore, the vectors representing the diagonals, denoted as ( \mathbf{d_1} ) and ( \mathbf{d_2} ), can be calculated as follows:

[ \mathbf{d_1} = \mathbf{a} + \mathbf{b} ] [ \mathbf{d_2} = \mathbf{a} - \mathbf{b} ]

Next, find the magnitudes of ( \mathbf{d_1} ) and ( \mathbf{d_2} ), denoted as ( |\mathbf{d_1}| ) and ( |\mathbf{d_2}| ), respectively.

After obtaining the magnitudes, we can use the dot product formula to find the angle between two vectors:

[ \cos \theta = \frac{\mathbf{d_1} \cdot \mathbf{d_2}}{|\mathbf{d_1}| \cdot |\mathbf{d_2}|} ]

Finally, calculate the angle ( \theta ) using the inverse cosine function:

[ \theta = \arccos \left( \frac{\mathbf{d_1} \cdot \mathbf{d_2}}{|\mathbf{d_1}| \cdot |\mathbf{d_2}|} \right) ]

Substitute the values of ( \mathbf{d_1} ), ( \mathbf{d_2} ), ( |\mathbf{d_1}| ), and ( |\mathbf{d_2}| ) into the formula to find the angle between the diagonals.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- In a parallelogram that is not a rectangle or rhombus, what is the probability of 2 randomly chosen angles being congruent?
- Two rhombuses have sides with lengths of #8 #. If one rhombus has a corner with an angle of #pi/6 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?
- What is the difference between a trapezoid and a rhombus?

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