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Question

What are cross product and dot product?

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Solution

Step-1:Cross product:Cross product is a binary operation on two vectors in three-dimensional space.The resultant vector of the cross product is perpendicular to both vectors.It is also called the vector product.The cross product of two vectors $\stackrel{\to }{A}$ and $\stackrel{\to }{B}$ is: $\stackrel{\mathbf{\to }}{\mathbf{A}}\mathbf{×}\stackrel{\mathbf{\to }}{\mathbf{B}}\mathbf{=}|\stackrel{\to }{A}||\stackrel{\to }{B}|\mathbit{s}\mathbit{i}\mathbit{n}\mathbit{\theta }\stackrel{\mathbf{^}}{\mathbf{\eta }}$ , where $\left|\stackrel{\to }{A}\right|,\left|\stackrel{\to }{B}\right|$ are the magnitudes of the vectors and $\theta$ is the angle between the vectors and $\stackrel{^}{\eta }$ is vector perpendicular to both vectors. Step-2: Dot product:The dot product is a scalar number obtained by performing a specific operation on the vector components.It is also called the scalar product.The dot product of two vectors $\stackrel{\to }{A}$ and $\stackrel{\to }{B}$ is: $\stackrel{\mathbf{\to }}{\mathbf{A}}\mathbf{·}\stackrel{\mathbf{\to }}{\mathbf{B}}\mathbf{=}|\stackrel{\to }{A}||\stackrel{\to }{B}|\mathbit{c}\mathbit{o}\mathbit{s}\mathbit{\theta }$ , where $\left|\stackrel{\to }{A}\right|,\left|\stackrel{\to }{B}\right|$ are the magnitudes of the vectors and $\theta$ is the angle between the vectors.

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