Multiplication of a vector by a scalar:

Given a vector and a scalar k ∈R, then k (or k) represents a vector whose magnitude is |k|||that is, k times that of and whose direction is same or opposite to that of  according as k > 0 or k < 0 respectively. Also, 0 = , null or zero vector which has zero magnitude and arbitrary direction.

            1 = , (-1) = -, etc.

When we have 2 vectors and such that = k, k ∈R, then and  are called as collinear vectors.  is said to be scalar multiple of .  and are parallel if k > 0 and anti parallel if k < 0.

Note that k₁ (k₂) = (k₁k₂) = k₂(k₁)∀ k₁, k₂ ∈ R.

A vector having magnitude as one (unity) is called as unit vector.

Unit vector in direction of  can be defined as 1/||. = /||and is represented by .

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