what is vecter product?

Question

i don,t know

Answer 1

Two methods of multiplying vectors exist.

Say you have two vectors, a = [a1 a2 a3] and b = [b1 b2 b3].

Dot product (also known as inner product):
Multiply the corresponding components of the vectors together, then add all of them. This gives a scalar value.
a . b = (a1*b1) + (a2*b2) + (a3*b3)
This works for vectors of any length.

Cross product (vector product):
The cross product is defined to return a third vector which is perpendicular to both argument vectors. Notice that the result is a vector; hence the name "vector product".

It only works for three-dimensional vectors. Rather than giving you the formula, I will show how it is derived. Otherwise, I doubt I could explain it.
Call the x, y, and z unit vectors i, j, and k. Using the right-hand rule, the following products are defined:
i * j = k, j * i = -k
j * k = i, k * j = -i
k * i = j, i * k = -j
i * i = 0, j * j = 0, k * k = 0

Using those products, we can break the vectors down and multiply:
a x b
= [a1 a2 a3] x [b1 b2 b3]
= (a1*i + a2*j + a3*k) * (b1*i + b2*j + b3*k)
= a1b1(i*i) + a1b2(i*j) + a1b3(i*k) + a2b1(j*i) + a2b2(j*j) + a2b3(j*k) + a3b1(k*i) + a3b2(k*j) + a3b3(k*k)
= 0 + a1b2k - a1b3j - a2b1k + 0 + a2b3i + a3b1j - a3b2i + 0
= (a2b3 - a3b2)i + (a3b1 - a1b3)j + (a1b2 - a2b1)k

So, as you can see, for the expression
c = a x b,
c1 = a2b3 - a3b2
c2 = a3b1 - a1b3
c3 = a1b2 - a2b1

There is a pattern, and it is fairly easy to memorize the equation, but it is much better to understand how and why it works... that way, if you forget the equation (ok, I will be perfectly honest: I had forgotten it), you can derive it (like I just did. horray.).

Answer 2

Vector are physical quantities which have both magnitude and direction.
Distance is not a vector.(it does not have a fixed specific direction)(it isa scalar)
Displacement is a vector(you have to specify initial an final positions. Hence it has a specific fixed direction.It also has a magnitude,a numerical value.)

Product of two vectors is called vector product.
It is of 2 types:-
1.Dot product:
Dot product between two vectors gives a scalar.
2.Cross Product
" between two vectors gives a vector quantity.