Vector Product: If we multiply a vector with any other vector or scalar quantity then the result is called vector product. Multiplying a vector by a scalar: If we multiply a vector by a scalar , then the result is a new vector. The magnitude of the vector formed by multiplying and , is the magnitude of multiplied by and the direction of the vector is same as vector if is positive and exactly opposite of is negative. And to divide the vector with we can simply multiply the vector with Multiplying a vector by a vector: We can multiply a vector with another vector in two ways as follows: Dot product or scalar product: The dot product or scalar product of two vectors and is defined to be: Where, is the angle between and . There are actually two angles between and one and another we can use either angle because their cosine is the same. The dot product or cross product of two vectors is a scalar and it is denoted by a dot in between two vectors, so the product is called dot product or scalar product. If vector and are denoted in component form then their dot product can be calculated as:
Vector Product:If we multiply a vector with any other vector or
scalar quantity then the result is calledvector product.Multiplying
a vector by a scalar:
If we multiply a vector by a scalar , then the result is a new
vector.
The magnitude of the vector formed by multiplying and , is the
magnitude ofmultiplied by and the direction of the vector is same
as vector if is positive andexactly opposite of is negative.
And to divide the vector with we can simply multiply the vector
withMultiplying a vector by a vector:
We can multiply a vector with another vector in two ways as
follows:Dot product or scalar product:
The dot product or scalar product of two vectors and is defined
to be:
Where, is the angle between and .
There are actually two angles between and one and another we
canuse either angle because their cosine is the same.The dot
product or cross product of two vectors is a scalar and it is
denoted by a dot inbetween two vectors, so the product is called
dot product or scalar product.
If vector and are denoted in component form then their dot
product can becalculated as:
Thus ,Cross product or vector product:
The cross product or vector product of two vectors and is a
third vectorwhose magnitude is given by:
where, is the smaller of the two angles between vector and .
And the direction of is perpendicular to both vectors andTo find
the exact direction of the cross product of vectors you can use
right hand rule ofvector products which stats if you make the
orientation of your right hand as shown thethe figure below then
the direction of your thumb is the direction of vector
:
The cross product or vector product is a vector quantity and is
denoted by a crossbetween two vectors, so the product is called
vector product or cross product.Note that the order of vector
multiplication is important because:
And if the vectors and are given in component form then their
cross product canbe calculated using the formula:
Multiplying a vector by a scalar:Dot product or scalar
product:Cross product or vector product:
