# The position vectors of the points A, B, C of a parallelogram ABCD are a, b, and c respectively. How do I express, in terms of a, b and, the position vector of D?

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The position vector of point D in terms of the position vectors of points A, B, and C in a parallelogram ABCD can be expressed using vector addition and subtraction. Since a parallelogram's opposite sides are parallel and equal in length, the vector representing the displacement from A to D will be the same as the displacement from B to C. Therefore, we can express the position vector of point D (( \vec{D} )) in terms of the position vectors of points A (( \vec{a} )), B (( \vec{b} )), and C (( \vec{c} )) as follows:

[ \vec{D} = \vec{B} + \vec{C} - \vec{A} ]

[ \vec{D} = \vec{b} + \vec{c} - \vec{a} ]

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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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- A line passes through #(4 ,3 )# and #(2 ,9 )#. A second line passes through #(7 ,1 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- An isosceles triangle has sides #a, b# and #c# with sides #b# and #c# being equal in length. If side #a# goes from #(2 ,9 )# to #(8 ,5 )# and the triangle's area is #64 #, what are the possible coordinates of the triangle's third corner?

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