Question

Define vector product. Explain the properties of a vector product with two examples​

Answer 1

Answer:

A vector is an object that has both the direction and the magnitude. The length indicates the magnitude of the vectors, whereas the arrow indicates the direction. There are different types of vectors. In general, there are two ways of multiplying vectors.

(i) Dot product of vectors (also known as Scalar product)

(ii) Cross product of vectors (also known as Vector product).

Properties of Vector Product

i) The vector product is do not have Commutative Property. It is given by,

a×b = – (b×a)

ii) The following property holds true in case of vector multiplication:

(ka)×b= k(a×b) =a×(kb)

iii) If the given vectors are collinear then

a×b= 0

(Since the angle between both the vectors would be 0, then sin 0 = 0)

iv) Following the above property

We can say that the vector multiplication of a vector with itself would be

a×a= |a||a|sin0 n^ = 0