# It is given #vec u=2vec i+3vec j # and #vec v=3vec i+2vec j # .How to calculate #vec u*vecv#?

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To calculate the dot product (also known as the scalar product) of two vectors, you multiply the corresponding components of each vector and then sum up the results.

Given vectors ( \vec{u} = 2\vec{i} + 3\vec{j} ) and ( \vec{v} = 3\vec{i} + 2\vec{j} ), the dot product ( \vec{u} \cdot \vec{v} ) can be calculated as follows:

[ \vec{u} \cdot \vec{v} = (2 \cdot 3) + (3 \cdot 2) ]

[ \vec{u} \cdot \vec{v} = 6 + 6 ]

[ \vec{u} \cdot \vec{v} = 12 ]

So, the dot product of ( \vec{u} ) and ( \vec{v} ) is 12.

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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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