prove-that-the-area-of-a-triangle-whose-two-sides-are-A-and-B-is-given-by-1-2-A-B-Also-find-the-direction-cosine-of-normal-to-this-area-Help-

Question Number 184656 by Mastermind last updated on 10/Jan/23

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{whose}\:\mathrm{two}\:\mathrm{sides}\:\mathrm{are}\:\overset{−} {\mathrm{A}}\:\mathrm{and}\:\overset{−} {\mathrm{B}}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{1}}{\mathrm{2}}\mid\mathrm{A}×\mathrm{B}\mid. \\ $$$$\mathrm{Also}\:\mathrm{find}\:\mathrm{the}\:\mathrm{direction}−\mathrm{cosine} \\ $$$$\mathrm{of}\:\mathrm{normal}\:\mathrm{to}\:\mathrm{this}\:\mathrm{area}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Answered by TheSupreme last updated on 10/Jan/23

$$\mid{A}×{B}\mid=\mid{a}\mid\mid{b}\mid{sin}\left(\theta\right) \\ $$

Commented by TheSupreme last updated on 10/Jan/23

$${direction}\:{normal} \\ $$$$\hat {{n}}=\frac{{A}×{B}}{\mid{A}×{B}\mid} \\ $$

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