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  • Show that the area of the triangle contained between the vectors a and b is one half of the magnitude of a × b.

Q7.4     Show that the area of the triangle contained between the vectors a\: and\: b  is one half
            of the magnitude of a\times b.

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best_answer

                                                     

Let a and b be two vectors having \Theta angle between them.

Consider \DeltaMON,

                                                    \sin \Theta \ =\ \frac{MN}{MO}

or                                                      \sin \Theta \ =\ \frac{MN}{\underset{b}{\rightarrow}}

or                                                         MN\ =\ b\sin \Theta

                                                       \left | a\times b \right |\ =\ \left | a \right |\left | b \right |\sin \Theta

                                                                         =   2 (Area of \Delta MOK)

                                                                       

Therefore the area of \Delta MOK  =   One half of      \left | a\times b \right |.

 

 

Posted by

Devendra Khairwa

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