.3 At which point P does the curve r(t) = ( 2t have the tangent vector (24, -8, 3) ? (a) P(2, 2, 2) сь) Р(-2, 2, - 4)

Q: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=<-5t5-3,4e-4t,-5sin(2t)>

Q: For the curve defined by F(t) = (e-t, 3t, e') find the unit tangent vector, unit normal vector,…

A:

Q: Q2. A particle is moving along the curve whose position vector is given as R(1) = (1) i + ( In…

A: Given

Q: Find the unit tangent vector to the curve defined by T(t) = (- 3t, 5t, V100 t) at t = 7. T (7) =

A: The given vector is: r→(t)=-3t, 5t, 100-t2

Q: Consider the two parametrized paths: r(t) = (t² + 7, t + 1, 25t-1), s(t) = (8t, 2t – 2, t² – 8) What…

A:

Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

A:

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: 3. Find the curve's unit tangent vector and find the length of the indicated portion of the curve:…

A:

Q: Sketch the graph of 7(t) = sin(t)i – 2cos(t)j–tk in 3-space; then find and draw the tangent vector…

A: Given, r→t=sinti^-2costj^-tk^

Q: a) By first sketching its projection onto the yz-plane, sketch the curve r(t) = (t, cos(t), 2…

A: For (a), We will plot the sketch of r(t)=t, cos(t), 2 sin(t),  0≤t≤4π onto the yz-plane (that means…

Q: 3. Find the unit tangent vector at t = T/2 for the following parametrized curve: F(t) = (cos 2t, 4,…

A: The given parametrized curve r→(t)=cos2t, 4, sin2t

Q: YouTrylt 4 Consider the path of a particle given by tangential and normal components of acceleration…

A: The position vector of the particle is given by  r(t) = 2t2, t3, -1

Q: 7) Find the unit tangent vector for the parameterized curve: r(t) = cos ti+ sin tj+ sin tk, 0≤t< 2π

A:

Q: Find the equation of the tangent plane to z=e^x+y+y^2+ 9 at the point (0,4,30)

A:

Q: Q.7: (A) Find the unit vector towards the tangent of the curve y = x at x =1

A: Find the unit vector towards tangent of the curve y=x2 at x=1.

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈1 − t^2, 5t, 2t^3〉, t = 2

A: r(t) =(1-t2, 5t, 2t3) at t=2

Q: 1. Show that the curve a(t) = (t,t² + 1, t – 1) is regular.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. Find the tangent vector to the curve 6t r(t) = [t3 – t, (2t + 1)*] t+1 at t = 1.

A:

Q: Find the Tangent vector, the Normal vector, and the Binormal vector (T, N and B) for the curve F(t)…

A:

Q: (A) Find A vector tangent and normal for the curve: x3 y = + 5 2 at the point (1, 5.5)

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: For the curve defined by F(t) = (e¯', 4t, e') find the unit tangent vector, unit normal vector,…

A:

Q: (a) Consider the curve C : r(t) = [t , –t², 2– t²]. Find a tangent vector, a unit tangent vector and…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

A: Answer

Q: x-1 y-2 z-1 2 -6 7 1 F(t) = ( 21 + ¹ )i + ¹/ (m² − 3)} j + t√21³-1k at t=1 1 4 (c) show that the…

A:

Q: 10. Draw the graph of the vector-valued functions (a) for the plane curve, r(t) = 2cost³i + 3sint³j,…

A:

Q: find a parametrization c(t) of the curve satisfying the given condition.  y = 3x − 4, c(3) = (2, 2)

A: To find the parametrization

Q: Find the unit tangent vector and the parametric equation of the line tangent to the given curve at…

A:

Q: Find the vector equation of the tangent line to F(e) = 2 (e1-t) in t i + tan"1tj+ k at cos(t ) the…

A: To determine the vector equation of the tangent line.

Q: Compute the tangent vector to the given path. c(t) = (2e", 2 cos(t))

A: The given path is: c(t)=(2et,2cos(t)) To find the tangent vector to the given path c(t).

Q: What is the slope at t = −2 ?

A:

Q: If the equation of the tangent plane to x2+y2-11z2=0 at (1,1, /2/11) is x+ay+Bz+y=0, then a+B+y=D

A: Given query is to find the equation of the tangent to the plane.

Q: b) Find the unit tangent vector for.. r(t) = at t=0

A: The unit tangent vector can be calculated using the formula T→(t)=r→′(t)‖r→′(t)‖. The denominator is…

Q: Compute the tangent vector to the given path. c(t) = (4t sin(t), 6t) %3D

A: The tangent vector for a vector r→t is r→'t.

Q: Determine an equation for the tangent plane to the graph of z = 2 2 +2 ay+2y2 - 4 at the point…

A:

Q: Find the unit tangent vector of the given curve. r(t) = 12t5i - 4t5j + 3t°k %3D

A: Given the vector function, r(t) , we call r′(t) the tangent vector provided it exists and provided…

Q: The vector parametric form of the tangent line to r(t) = (3t², ¿, t – 1) at t = -5 is

A:

Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

A:

Q: x-1_y-2_z-1 -6 (c) show that the line 2 7 curve F(t) = (21+²) 1+ ²+ (in ²²-3) 1+1√21³²-1k at 1=1 i+…

A:

Q: Find an equation for the tangent plane to the graph of z = xe' cos z – 2 - at the point (2,0,0). 1.…

A:

Q: Find the vector equation of the tangent line to F(t) = 2 (el-t) In t i+ tan-tj+ k at cos(t m) the…

A: Answer is mentioned below

Q: 4. Let g(x, y) = e"/v, Find an equation for the tangent plane at (x, y) = (2, 1).

A:

Q: 2. Consider the function 7(t) = (t² - 4, t – 2, v80 + 4t + 7t² - t*). imothy e startin Find…

A: Given, x= t²-4 y= t-2 z= √(80+4t+7t²-t⁴) (xp,yp,zp)= (-3,-1,√90)

Q: 1. Find the tangent vector to the curve 6t r(t) = [t³ – t, t+1 , (2t + 1)*] at t = 1.

A: As per our guidelines we are supposed to answer only one question. If you want solution of any…

Q: A bee with velocity vector r'(t) starts out at (-3, 2, 4) at t = 0 and flies around for 9 seconds.…

A:

Q: find unit tangent vector of the given curve r(t)=(4-2t)i+(2t-3)j+(8+t^2)k

A:

Q: Find the point on the graph of z = 3x2 – 3y? at which vector n = (48, –60, –2) is normal to the…

A:

Q: Find the unit tangent vector to the curve r(t) = (2sin(t),2cos(t)) at the points t =-n, t=0 and t…

A:

Q: (iii) Find a vector equation for the tangent line to the curve of intersection of the cylinder a² +…

A:

Q: 1. Find the tangent vector to the curve 6t r(t) = [t° – t, (2t + 1)*] at t = 1.

A:

Q: Find the tangent vector of r(t) = (t° , 3tª) at time t = 1. A) (3, 12) B) 15 C) (3, 7) D) 3t2 + 12t3

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.