Question

Why we took cosፀ in a.b (scalar dot product)

Answer 1

Answer:

Dot product basically tells the similarity between the two types of vectors or say how much they are likely.We can say that it is defined as how the two vectors are similar to each other.Suppose that the two author’s have written their theories and the content is almost same. So if now we represent the two theories as vectors We can find how similar they are by the Dot product of the two theories let’s say A1.B1.

Two vectors are similar if they are very close to each other or completely different if they are Perpendicular to each other.

Now suppose the two vectors are exactly similar.

So their dot product must represent the correct closeness or a.b=a^2 or b^2.

Now if the angle between them is sin(theta) then sin(0)=0. So that represents the two completely different vectors rather then similar vector.

That’s why the dot product a.b=ab cos(theta) as cos(0)=1 and hence represent the two very similar vectors and the same is case with the cross product which represent the two completely different vectors.