The discussion centers on the computation of the scalar projection of vector \( a \) onto the cross product \( a \times b \). The formula used is \( \text{comp}_a(a \times b) = \frac{a \cdot (a \times b)}{|a|} \), which simplifies to zero due to the properties of the dot product and cross product. The conclusion is that the scalar projection is indeed zero, confirming that the vectors \( a \) and \( a \times b \) are orthogonal. Additionally, the discussion highlights the validity of interchanging dot and cross products in a triple scalar product.
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Your work is correct assuming that you have proven the formula that you can interchange dot and cross in a triple scalar product:$$hnnhcmmngs said: