IIT JEE , AIEEE Forum - Physics , Mechanics

mukundeng12

show that area contained between two vectors a and b is equal to one half of magnitude of a x b

edison

Consider a triangle ABC

Here AB = Vector a

AC= Vector b

Let angle between a and b be

Drop a perpedicular from point B on AC, say it is BD

Length of the perpendicular = BD = a sin

Therefore, area of the triangle ABC= (1/2) base * altitude = (1/2)*AC * BD

area between vectors a and b = area of triangle ABC = (1/2)*b*a sin

area between vectors a and b =(1/2)*b*a sin

= (1/2) of magnitude of (a x b)

mukundeng12

Thanxxxxxx a lot