What is the product of vector and scalar?

Answer 1

The scalar product of two perpendicular vectors is zero.

In classical mechanics we define the scalar product between two vector a and b as:

a · b = |a| |b| cos(alpha)

where |a| is the modulus of vector a and alpha is the angle between vectors a and b.

If two vectors are perpendicular, alpha equals 90º (or PI/2 rad) and cosine of alpha is, consequently, zero.

So finally a · b = 0.

Answer 2

The product of a vector and a scalar is a new vector whose magnitude is the product of the magnitude of the original vector and the scalar, and whose direction remains the same as the original vector if the scalar is positive or in the opposite direction if the scalar is negative.

Answer 3

A vector: the scalar portion of the vector is multiplied with the scalar, but the direction is 'conserved' - it just changes the amount, not the direction.