Use Newton's Second Law of Motion to find the force required so that a particle of mass 2 has position r(t) = (t2,t*, sin(2t)) %3D Select one: a. (2, 12t2,-4 sin(2t)) b. (4, 2412,-8 sin(20;, c. 28 d. 24 e. (2t, 4t,2 cos(2t))

Q: y = In x3 sinx 2 Cx² + 4

A: The function is given by y = lnx3sinxx2+4 To evaluate: The expression of dydx.

Q: cos r In(sin a)dx

A:

Q: An object is moving along the coordinate line with velocity v(1) = 5 cos t, 0 < x s 2x. What is the…

A:

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to 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.