In this section we will study on multiplication(Product) of vectors.

PRODUCT OF TWO VECTORS:-

this is of two types

i)Scalar Product

ii)Vector Product

=>>Scalar Product-

When product of two vectors is a scalar quantity,it is called ‘Scalar Product’.

If a & b be two vectors then their scalar product is denoted by ‘a.b’ and

a.b=|a||b|cos@ or

a.b=lmcos@

(`.`|a|=l etc.)

Important for a.b

i)a.b=b.a

ii)a.a=|a|2=l2

iii)a.b=0 =>a¿b

iv)i.i=j.j=k.k=1

i.j=j.k=k.i=0

v)if a=pi+qj+rk and

b=si+tj+uk ,

then

a.b=ps+qt+ru

vi)cos@=a.b/lm

=>>Vector Product-

when product is a vector quantity,it is called ‘Vector Product’.

It is written as ‘a*b’ and

a*b=|a||b|sin@ñ

a*b=lmsin@ñ

where ñ is u.v. along

a*b

Important for a*b

i)a*b=-b*a i.e. a*b is not equal to b*a

ii)a*a=0

iii)a*b=0 =>a || b

iv)i*i=j*j=k*k=0 ,and

i*j=k

j*k=i

k*i=j

v)a*b=

[i j k]

|p q r|

[s t u]

vi)if a & b are adjacent sides of ||gm, area of ||gm= |a*b|, and if sides of triangle then area=half of |a*b| i.e. Area=|a*b|/2

vii)if a and b are diagonals of ||gm ,area=|a*b|/2

viii)sin@=|a*b|/lm