area of base of parallelepiped (parallelogram) = b ×c. the vector b ×c will be perpendicular to base. therefore: volume of parallelopiped = area of base × height = (b ×c) × A cos θ = a ⋅ (b ×c) …
$\begingroup$ @user3180 The argument is complete: if we accept that 1) For a cuboid the volume is given by the (absolute value) of the determinant of the corresponding diagonal …
Volume of a n dimensional parallelepiped in n dimensional space is given by the determinant of the n by n matrix formed by it's edge vectors. Which makes sense considering that unit axis …
I am trying to find the rectangular parallelepiped of greatest volume for a given surface area S using Lagrange's method. I tried solving by myself but at x=y=z = a, I am not getting …
$\begingroup$ Good, but there is a mistake in the picture: it seems to suggest that the face the contains $\mathbf a$ and $\mathbf c$ is vertical, while it's not true in general, and the …
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