1)Why the dot product of two vectors is scaler?

Answer 1

Because the dot product HAS to be a real number, which is also known as a scalar number.

for example:

[2 5 -7] [6 -2 -5] = (2)(6) + (5)(-2) + (-7)(-5) = 12 + (-10) + 35 = 37

37 is a real number, i.e. a scalar number.
dot product will always be a scalar.

Think of it like this:

If you drive from your home to the grocery store, you've traveled a real distance, say 5.3 miles.

That 5.3 miles is a real number, a scalar number.

this is just the way it works :)

Answer 2

i think of it is going something like this AB = (5, 4, 2) - (3, 2, a million) = (2, 2, a million) AC = (-4, 2, a million) - (3, 2. a million) = (-7, 0, 0) Scalar Product = (2 x -7) + (2 x 0) + ( a million x 0) = -14 + 0 + 0 = -14

Answer 3

dot product is defined as the projection of one vector over other. its only a length. so it is scalar

Answer 4

In addition to what other have said here;
We use dot product in Physics to express a physical quantitiy that is independent of the co-ordinate system.
eg. work done.

Answer 5

Hope the following web pages will be helpful to you:


http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

Answer 6

Because that's how we defined it.

Answer 7

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