Multiplying a vector by a scalar 2d

Introduction to Scalar Multiplication in 2D Vectors

A scalar is a single numeral, often used in mathematics to scale, or multiply, vectors.
Multiplying a vector by a scalar entails increasing or decreasing the vector’s magnitude without changing its direction, unless the scalar is negative, in which case the direction is reversed.
The result of scalar multiplication is a new vector whose direction is the same as the original vector (or exactly opposite if the scalar is negative) and whose magnitude is the magnitudes of the original vector times the absolute value of the scalar.

Scalar Multiplication: Method and Result

To multiply a vector by a scalar, each component of the vector is multiplied by the scalar.
For instance, if a 2D vector is represented as [a b], then multiplying this vector by a scalar k would result in [ka kb].
If the scalar is negative, the resultant vector will point in the opposite direction of the original vector.

Illustrations of Scalar Multiplication

If k>1, the resultant vector will be an enlargement of the given vector.
If 0<k<1, the multiplication will produce a smaller version of the original vector.
If k=1, the resultant vector will be the same as the original one.
If k=0, the result is a zero vector, [0, 0], which has no direction or magnitude.

Remember, understanding scalar multiplication is vital for dealing with problems in geometry related to scaling, rotations, reflections, and transformations.