Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) = (5t, 5 sin(t), cos(5t)) v(0) = (0,3, 4) 7(0) = (0, –3, –4) Find: 7 (t).
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.
We have acceleration, initial velocity, and initial position, and if we integrate acceleration with respect to time we get velocity, similarly, if we integrate velocity with respect to time we get displacement. From this, we can find our position vector with the inputs from the initial position vector values.
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