Sketch the curve represented by the vector-valued function                              r(t) = (t + 1)i + (3t − 1)j + 2tk and give the orientation of the curve.

Q: Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval…

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: Surfaces z = x² + 2y², x + y = 0 X Parameter x = 5t

A:

Q: Sketch the vector-valued function r(t) = ⟨cos(t), 1, sin(t)⟩,

A: Sketch the vector-valued function r(t) indicating the orientation of the curve with an arrow.…

Q: Represent the line segment from P to Q by a vector-valued fur P corresponds to t = 0. Q corresponds…

A:

Q: Let F(x,y, z) = rye" – 2² Jī and P(1,0, –1).

A: Given Fx,y,z=xyey-z2x and P1,0,-1Vector u=⟨2,-3,6⟩

Q: sketch the space curve represented by the vector- valued function and give the orientation of the…

A: The given curve are (i) r(t)=-t+1i+4t+2j+2t+3k. (ii) r(t)=t,t2,23t3. To Sketch: The given curves…

Q: Sketch the graph of the vector-valued function F(t) = (2t – 1)² î +(2t +2) ĵ. Draw arrows on your…

A: The vector valued functions in two dimensions can be represented as r→(t)=x(t)i^+y(t)j^.

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.