The position vector r of a particle at time t is r = 2t°i + (t – 4t)j+ (3t – 5)k. Find the velocity and the acceleration of the particle at time t. Show that when t = 2/5 the velocity an the acceleration are perpendicular to each other. The velocity and the acceleration are resolved into components along and perpendicular to the vector i- 3j + 2k. Find the velocity and acceleration components parallel to this vector when t = 2/5.

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.