= λ a + µ b where λ and µ are real numbers. . A unit vector associated with a vector A has magnitude and is along the vector A : ˆ n The unit vectors ɵ ɵ i, j, k are vectors of unit magnitude and point in the direction of the x-, y -, and z- axes, respectively in a right-handed coordinate system. .
A vector A can be expressed as i + = A where A x , A y are its components along x- , and y - axes. If vector A makes an angle θ with the x -axis, then A x = A cos θ , A y = A sin θ and , tan . . Vectors can be conveniently added using analytical method .
If sum of two vectors A and B , that lie in x-y plane, is R , then : ɵ , where, R x = A x + B x , and R y = A y + B y . The position vector of an object in x-y plane is given by r and the displacement from position r to position r’ is given by ∆ r = r ′ − r ′ − ′ − = ∆ + ∆ . If an object undergoes a displacement ∆ r in time ∆ t , its average velocity is given by v = . The velocity of an object at time t is the limiting value of the average velocity as ∆ t tends to zero : v = ∆ t → .
It can be written in unit vector notation as : ɵ where , , When position of an object is plotted on a coordinate system, v is always tangent to the curve representing the path of the object. . If the velocity of an object changes from v to v ′ in time ∆ t , then its average acceleration is given by: a v' The acceleration a at any time t is the limiting value of a as ∆ t