cross product

Consider two vectors $\rm \vec a = 5 i + 7 j + 2 k $ $\rm \vec b = 3i - j + 6k$ Magnitude of the component of $\vec a$ orthogonal to $\vec b$ in the plane containing the vectors $\...

A triangular facet in a $$CAD$$ model has vertices: $${P_1}\left( {0,0,0} \right);\,\,{P_2}\left( {1,1,0} \right)$$ and $$\,{P_3}\left( {1,1,1} \right).$$ The area of the facet is

The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ is