Q.For two vectors to be equal, they should have the (A) same magnitude (B) same direction (C) same magnitude and direction (D) same magnitude but opposite direction

Physical quantities fall into two fundamental classes. A scalar quantity is completely specified by a magnitude alone — a number together with a unit — with no reference to direction; mass, time, temperature, density, and distance travelled are all scalars, and they combine using the ordinary rules of algebra. A vector quantity needs both a magnitude AND a direction for its complete description; displacement, velocity, force, and momentum are common examples.

A vector is represented geometrically by a directed line segment (an arrow) drawn to scale, with its length giving the magnitude and its orientation giving the direction; the starting point is called the tail and the arrowhead end is called the head. Several named types of vectors recur throughout physics: the zero (null) vector, which has zero magnitude and an arbitrary direction (e.g. the velocity of a stationary body); the resultant vector, the single vector equivalent to two or more vectors acting together; the negative vector, which has the same magnitude as a given vector but points in exactly the opposite direction; equal vectors, which must share both the same magnitude and the same direction; the position vector, which locates a particle relative to a chosen origin; and the unit vector, a vector of magnitude exactly 1 obtained by dividing any non-zero vector by its own magnitude, $\hat u_M = \vec M/|\vec M|$.

In a rectangular coordinate system, the unit vectors along the x, y, and z axes are denoted $\hat i$, $\hat j$, and $\hat k$ respectively, and every vector can be expressed in terms of these — the foundation for resolving vectors into components and for the algebraic (component) forms of vector addition and multiplication.