A vector is a directed line segment characterized by both magnitude and direction. In JEE, vectors are primarily represented in component form: a = $a_{1}$i + $a_{2}$j + $a_{3}$k, where i, j, k are mutually perpendicular unit vectors along the x, y, z axes respectively. The magnitude is |a| = sqrt($a_{1}^{2}$ + $a_{2}^{2}$ + $a_{3}^{2}$). A unit vector (magnitude 1) in the direction of a is a-hat = a/|a|. The zero vector 0 has zero magnitude and no definite direction. Two vectors are equal if and only if all their corresponding components are equal. Position vectors represent the vector from the origin to a point: the position vector of point P(x, y, z) is xi + yj + zk.