Q. 43.6( 30 Votes )

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

Answer :

Consider two vectors (OK) and (OM) are making angle θ which each other as shown in following figure,



Now,


In ΔOMN we can write the equation,




We know that magnitude of cross product of vectors a and b is,



= ()


= ×OK×MN ( = 1)


= 2×Area of ΔOMK


Area of ΔOMK =


Hence Proved.


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