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[Page 4] Vectors 1 Introduction of Vector Physical quantities having magnitude, direction and obeying laws of vector algebra are called vectors. Example : Displacement, velocity, acceleration, momentum, force, impulse, weight, thrust, torque, angular momentum, angular velocity etc. If a physical quantity has magnitude and direction both, then it does not always imply that it is a vector. For it to be a vector the third condition of obeying laws of vector algebra has to be satisfied. Example : The physical quantity current has both magnitude and direction but is still a scalar as it disobeys the laws of vector algebra. Types of Vector (1) Equal vectors : Two vectors A and B are said to be equal when they have equal magnitudes and same direction. (2) Parallel vector : Two vectors A and B are said to be parallel when (i) Both have same direction. (ii) One vector is scalar (positive) non-zero multiple of another vector. (3) Anti-parallel vectors : Two vectors A and B are said to be anti-parallel when (i) Both have opposite direction. (ii) One vector is scalar non-zero negative multiple of another vector. (4) Collinear vectors : When the vectors under consideration can share the same support or have a common support then the considered vectors are collinear. (5) Zero vector ) 0 ( : A vector having zero magnitude and arbitrary direction (not known to us) is a zero vector. (6) Unit vector : A vector divided by its magnitude is a unit vector. Unit vector for A is A ˆ (read as A cap or A hat). Since, A A A ˆ A A A ˆ . Thus, we can say that unit vector gives us the direction. (7) Orthogonal unit vectors j i ˆ , ˆ and k ˆ are called orthogonal unit vectors. These vectors must form a Right Handed Triad (It is a coordinate system such that when we Curl the fingers of right hand from x to y then we must get the direction of z along thumb). The x x i ˆ , y y j ˆ , z z k ˆ i x x ˆ , j y y ˆ , k z z ˆ (8) Polar vectors : These have starting point or point of application . Example displacement and force etc. (9) Axial Vectors : These