Q. What is the formula for volume of a tetrahedron whose vertices are given by the vectors a, b, c, d
Q. How to decide whether a system of planes can form a prism or not?
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4 Answers
1i guess if i m rem correctly
volume=\frac{1}{6}\left [ \vec{b}-\vec{a} \; \;\; \; \vec{c}-\vec{a} \; \;\; \; \vec{d}-\vec{a}\right ]
a system of planes can form a prism only wen none of any two pair of planes out of them r parallel to each oder
62The proof for the expression given in Q 1 is as simple as this...
The volume is given by 1/6 (Area of base) x (Height)
Area of the base is the cross product of the two sides of the base..
while the perpendicular height can by found by using the dot product of the area vector with any of the other sides.
I hope that makes the expression given in #2 clearer..
