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

Answer 1

Sophie Adams

#vecu*vecv=((6),(6))=6i+6j#

#vecu=((2),(3))# and #vecv=((3),(2))#

The dot product is given by #veca*vecb=((a_ixxb_i),(a_jxxb_j),(vdotscolor(white)(xx)vdots))#

#vecu*vecv=((2xx3),(3xx2))=((6),(6))=6i+6j#

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Answer 2

Xavier Alonso

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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Answer from HIX Tutor

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.