the vector function r ( t ) = ⟨ 6 cos ⁡ ( t ) , 3 − 3 sin ⁡ ( t ) , 2 + 3 sin ⁡ ( t ) ⟩ 1.Find the equation of the line tangent to the space curve at ( 0 , 2 , 3

Q: (9.) r(t) = (1, cos t, 2 sin t)

A: As per your query the solution of question no 9 is given the next step.

Q: 5. Let 0 be the angle between vectors ū = (1,3) and i = (5, 2). What is cos 0 and what is sin 0?

A: Angle between two vectors is given by,

Q: Let the velocity vector be v(t) = (4t°, –6 sin(3t) , 9 exp(3t)) and the initial position vector be…

A: The position vector can be computed by taking the summation of velocity vector and initial position…

Q: Find the set of parametric equations for the tangent line to the graph of the vector-valued function…

A: To find the set of parametric equations for the tangent line to the R(t)=<t+sin3t, t+cos3t,…

Q: 2. For this entire page, let r(t) = (4 sin(t), 3t, 4 cos(t)) (a) Circle the correct graph for the…

A: The objective of this question is to understand the properties of the vector function r(t) = (4…

Q: Given the vector function (1) = (e+²³, 2√²³ +1, 4arctan(1 − 1)) 1)), find the speed and the equation…

A:

Q: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

Q: Find a vector parametric equation F(t) for the line through the points P = (1,0,-5) and Q=(2,3,-7)…

A: The vector parametric equation of the line that passes through the points: A=x1, y1, z1, B=x2, y2,…

Q: 2) Let two vector functions be defined by r₁(t) = (2t, t², t²) r₂(t) = (sint, sin(3t),5t) a. Find…

A: a. Consider the given vector functions, r1(t)=2t,t2,t4r2(t)=sint,sin3t,5t if two vector function…

Q: Identify the direction from graph of functions given below: vector i) r = i(2 cos 21)+ j(2sin 2r) ;…

A: Given, r→=i^(2cos2t)+j^(2sin2t) Identify the direction vector, From the given position vector,…

Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

A:

Q: (3.) (a.) (Circle the correct choice) Which of the following vector functions describes a circle of…

A:

Q: Determine the equation of the tangent plane and a vector equation of the normal line to A. tangent…

A:

Q: 3. Find an equation of the plane tangent to the Bohemian dome S described by the vector function…

A:

Q: 2) Consider the vector function r(t) = (sin (t), −3t, cos (t)). Analyze the function, then sketch a…

A: The given function is r(t)=sinπ2t,-3t,cosπ2t Find the value of r(t) for different values of t. t…

Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

A:

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.