|FSc part 1 Physics|#scalarproduct or dot product|characteristics of scalar product|in Urdu Hindi|

*Scalar product or dot product*
If the product of two vectors is a scalar quantity is called scalar product.
A and B are two vectors.
A . B= ABcosx
Physical meaning..
Dot product of two vectors is equal to the magnitude of first vector and component of second vector.
A. B= A(projection of B on A.
A. B = A(Bcosx)
Now
B . A = B(Acosx)
*Examples*
W= F . D
P= F. V
*Characteristics of scalar product*
1_ Commutative property.
Scalar product of two vectors is Commutative.
A.B= B.A
2_prependicular vectors..
If two vectors are matually prependicular then their scalar product is zero.
A.B= 0
3_ parallel and antiparallel..
If two vectors are parallel their scalar product is equal to their magnitude.
A.B= AB
When antiparallel product is negative.
A.B= - AB
4_ self scalar product..
Self square product is equal to it's square of it's magnitude.
A.A= A²
In case of unit vectors.
î.î = 1
Similar for j and k.
5_ scalar product in term of rectangular components..
Two vectors are in space or 3_D..
ABcosx= Ax Bx + AyBy +Az Bz / AB
X = cos- (AxBx +AyBy +AzBz)/AB
This equation can be use to find the angle between two vectors.
#scalarproduct
#Dotproduct
#characteristics