What are the different methods to calculate vector products?

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Different methods to calculate vector products include the determinant method using the standard unit vectors i, j, and k, as well as the component method involving the formula AxB = i(a2b3 - a3b2) + j(a3b1 - a1b3) + k(a1b2 - a2b1). Another approach involves using the angle between the two vectors, which can be applied in various problems. These methods are mathematically equivalent and yield the same results for vector cross products. Understanding these techniques is essential for solving vector-related problems effectively.
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Ways to find vector products??

Homework Statement



can any1 tell me diferent ways to find vector products?

Homework Equations





The Attempt at a Solution


i know this one
AxB=i(a2b3-a3b2)+j(a3b1-a1b3)+k(a1b2-a2b1)
 
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There is the way involving the angle between the two vectors (which you have used in some other problems you posted here.)
 


Wikipedia says:
\mathbf{a}\times\mathbf{b}= \begin{vmatrix}<br /> \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\<br /> a_1 &amp; a_2 &amp; a_3 \\<br /> b_1 &amp; b_2 &amp; b_3 \\<br /> \end{vmatrix}
:smile: (but that's equivalent to what you already mentioned)
 
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