Why does multiplying two vectors make a scalar?

5 Answers. No, it doesn’t give another vector. It gives the product of the length of one vector by the length of the projection of the other. This is a scalar.

Does multiplying 2 vectors give you a scalar?

Dot product – also known as the “scalar product”, a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the magnitudes of the two vectors and the cosine of the angle between the two vectors.

When you multiply a vector by a scalar the result is?

When multiplying a vector by a scalar, the direction of the vector is unchanged and the magnitude is multiplied by the magnitude of the scalar. This results in a new vector arrow pointing in the same direction as the old one but with a longer or shorter length.

Why the dot product of two vectors is scalar whereas the cross product of two vectors is a vector?

The dot product is defining the component of a vector in the direction of another, when the second vector is normalized. As such, it is a scalar multiplier. The cross product is actually defining the directed area of the parallelogram defined by two vectors.

What is the rule for scalar multiplication of vectors?

To multiply a vector by a scalar, multiply each component by the scalar. If →u=⟨u1,u2⟩ has a magnitude |→u| and direction d , then n→u=n⟨u1,u2⟩=⟨nu1,nu2⟩ where n is a positive real number, the magnitude is |n→u| , and its direction is d .

What is scalar multiplication?

Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).

How do you know if two vectors are scalar multiples?

We note that the vectors V, cV are parallel, and conversely, if two vectors are parallel (that is, they have the same direction), then one is a scalar multiple of the other. Q1. There is an implication in the statement that two vectors are parallel if they are in same direction.

Can two vectors of same magnitude have resultant equal to either of them explain?

Two vectors (inclined at any angle) and their sum vector from a triangle. Thus, the vector →A and →B of same magnitudes have the resultant Vectors →R of the same magnitude. In this case angle between →A and →B is 120∘.