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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