What is dot product and how to calculate it?

There are two ways of multiplying vectors: one gives you another vector (cross product) and the other gives you a scalar- a number, like 3, 18 or 196 352. Hence, dot product is also called the scalar product.Imagine two vectors X=(a, b, c) and Y=(d, e, f). The first number gives you length of the vector in the x direction, second tells you its length in the y direction and third gives you the z direction. The easiest way to find the dot product is done by multiplying the numbers in the i, j and k rows of both vectors and then adding the results together. So, on the example of X and Y: X.Y=ad+be+cf.Another example: A=(1, 5, 9) and B=(0, -6, 4). The dot product of A and B: A.B= 10 + (5-6) + (4*9) = 0 - 30 + 36 =6.Dot product can also be used to find the angle between two vectors. The full formula for dot product between X and Y is: X.Y = |X| |Y| cos(x). Where 'x' is the angle between both vectors and |X| and |Y| are the lengths of vectors X and Y. The length can be found using the formula: |X| = sqrt(a²+b²+c²).