Page 36 - Electrostatics-11

© GC Shiba

1) Scalar product ( dot product)
⃗
⃗⃗
The scalar product of two vectors and is defined as
⃗ ⃗⃗
. =
⃗⃗
⃗
Where is the angle between vectors and .

2) Vector product ( cross product)
⃗
⃗⃗
The vector product of two vectors and is defined
⃗⃗
⃗
as × =
̂
⃗
Where is the angle between vectors and
⃗⃗
.
is unit vector perpendicular to the plane
̂
⃗⃗
⃗
containing both and .
Note:
a. The dot product of two vectors is a scalar.

⃗⃗ ⃗
⃗ ⃗⃗
i.e., . = .
b. The cross product of two vectors is a vector.
⃗⃗
⃗⃗
⃗
⃗
i.e., × = − ×

Geometrical meaning of cross product:

Area of parallelogram OPQR = Base x
perpendicular distance

= × =

⃗
⃗⃗
, × =
Hence, the area of parallelogram OPQR is equal to the magnitude of cross product
of two vectors which are represented by two adjacent sides of parallelogram.

13 Mechanics