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jdawg
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Homework Statement
The value of 3i(dot)(jxk)
Homework Equations
The Attempt at a Solution
I know the answer is 3, but could someone please explain how to work this problem?
The dot product is a mathematical operation that takes two vectors and returns a scalar quantity, while the cross product takes two vectors and returns a vector quantity. The dot product measures the similarity or projection of one vector onto another, while the cross product measures the perpendicularity or rotation of one vector from another.
The dot product of two vectors, A and B, is calculated by multiplying the corresponding components of the vectors and then summing the results. In other words, A ∙ B = AxBx + AyBy + AzBz.
The cross product of two vectors, A and B, is calculated by taking the determinant of a 3x3 matrix formed by the two vectors and the unit vectors i, j, and k. In other words, A x B = i(AyBz - AzBy) - j(AxBz - AzBx) + k(AxBx - AyBx).
The dot product can be interpreted geometrically as the product of the magnitude of one vector and the length of the projection of the other vector onto the first. This can be visualized using the formula A ∙ B = |A||B|cosθ, where θ is the angle between the two vectors.
The cross product can be interpreted geometrically as the area of the parallelogram formed by the two vectors. This can be visualized using the formula |A x B| = |A||B|sinθ, where θ is the angle between the two vectors.