the curve with the given vector equation. Tndicate with an arro w the direction in which t ncreases r(t) = (t, 8 - t, 2t)

Q: At which point P does the curve r(t)=( 2t, 4t+1, t’) given in vector form have the tangent vector…

A: Given: To explain the correct option of the given statement as follows,

Q: The position vector of a particle is r(t). Find the requested vector. The velocity at t 0 for r(t)…

A:

Q: 2. (a) Calculate the position vector for P₁ and the displacement vector from P₁ to P₂, where P₁:…

A:

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

A: Here we have, the given curve is r→(t)=2t3, 2t2, 3t-1                now differentiate with respect…

Q: Find a vector parametric equation r(t)|for the line through the points P = (-3, –2)|and Q = (-5,…

A: According to the problem, we have

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: To indicate the direction in which t increases and sketch the graph of the vector function given…

Q: Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t…

A: Topic = vector

Q: Find all values of t for which the tangent line to the curve r(t) = (2t – t,t - t²) is orthogonal to…

A: Find the solution below

Q: The length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the…

A: Given information: Parametric equation of curve is : x=x(t)y=y(t)z=z(t) We need to find the length…

Q: Given 7(t) = (t - 2, t + 1), t = -1: a. Sketch the plane curve with the given vector equation. b.…

A:

Q: Q2) Find the vectors the curve r(t) = at the point (11) of

A: First of all find r'(t) and the length of r'(t). Here, r'(t)=<2t,2t2,1> |r'(t)|=4t2+4t4+1…

Q: Q3. The position vector of a particle in space is given as R = (1.25 t2) i+ (t)j. Find the Normal…

A: The position vector is given as R=(1.25t2)i +t3j . Hence, x=1.25t2 , y=t3    Next find the value of…

Q: 5) Consider the vector function r = (9 — 2t, 4 + 2t, √√2t²) a. Find the length of the path on 0≤t≤1.…

A: Given,

Q: 1. Given that r(t) = t²i+tj + 2k. Sketch the curve with the given vector equation. Indicate with an…

A:

Q: Find T, N, and B for the curve r(t) = (10t, 10t, e') at (0,0, 1). Hint: After finding T', plug in…

A:

Q: Please answer the following question Find the vector equation of a line L going through the points…

A: Determine the direction vector m for the line L going through the points (-3,-1) and (-4,3).…

Q: At which point P does the curve r(t) =( 2t2, 4t+1, t³ ) given in vector form have the tangent vector…

A: Given, r(t)→=2t2,4t+1,t3  tangent vector 4,4,3 we know derivative of vector valued function gives…

Q: At which point P does the curve r(t) = ( 21°, 21°, 3t – 1) given in vector form have the tangent…

A: Given r→(t) = 2t3 , 2t2 , 3t-1 Then r→'(t) = 6t2 , 4t , 3 Tangent vector at a point is given as 24 ,…

Q: Consider the following graph. (4, 4) 2 (1, 2) 1 3 (a) Find the component form of the vector v. (v,,…

A:

Q: At which point P does the curve r(t) = ( 21?, 4t +1, t) given in vector form have the tangent vector…

A: Given equation of curve as, r→(t)=2t2,4t+1,t3.

Q: A laser’s beam shines along the ray given by r1(t) = (1, 2, 4) +t(2, 1, −1) for t ≥ 0. A second…

A: Given :         r1(t) = (1, 2, 4) + t(2, 1, -1) for t ≥ 0        r2(s) = (6, 3, -1) + s(-5, 2, c)…

Q: Find a vector equation and parametric equations in t for the line through the point and…

A: Given that the point that posses through the line and the line perpendicular to the plane is, P 0 =…

Q: C:r=r(t)=(1+t,2 – 3t, 4t)

A: We Have :— X = 1 + t Y = 2 — 3t Z = 4t

Q: Find all values of t for which the tangent line to the curve r(t) = (3t – t°,t –- t²) is orthogonal…

A: Given curve is

Q: r(1) = 1²i + t*j + 1°k

A: we can find some points and draw a curve passing through these points…

Q: The position vector of an object at time t is given by: r = (at -31 )i+(6t² -bt)j Find the speed of…

A: the given position vector is r=at3-3t2i+6t2-btj to find the speed of the object  first find the…

Q: Consider the following graph. (4, 5) (1, 3) 1. (a) Find the component form of the vector v. (V, V2)…

A: Given a graph showing the vector.

Q: Find T, N, and B for the curve r(t) = (14t, 14t, e') at (0, 0, 1). %3D Hint: After finding T', plug…

A:

Q: L(t) The vector parametric equation for the line through the points (1, 2, 4) and (5, 1,-1) is

A: Given points,  (1,2,4) and (5,1,-1)

Q: The path of a particle is moving in the plane with position vector . What is the speed of the…

A:

Q: Given the vector function 7(1)=(31²-1, 1-8√F³, 12t-4), find the speed & arc length of the curve on…

A:

Q: Q3. The position vector of a particle in space is given as R = (1.25 t2) i+ (t³)j. %3D Find the…

A: The position vector of a particle is given as R = (1.25 t2) i + (t3) j   The normal vector at point…

Q: At which point P does the curve r(t) = ( 2t2, 4t +1, t³ ) given in vector form have the tangent…

A:

Q: Show that the curve with vector equations ~r(t) = is a plane curve

A:

Q: B) The vector v = (3cost)i + (3sint)j +t2k .gives the position of a moving body at time t. find the…

A:

Q: (a) Sketch the plane curve with the given vector equation. (b) Find r'(1). (c) Sketch the position…

A: A.

Q: Consider the following graph. (4,5) 2 (1, 2) 3 (a) Find the component form of the vector v. (b)…

A: Given vector is as shown below :

Q: At which point P does the curve r(t) = ( 2t+3, 3t², t* ) given in vector form have the tangent…

A:

Q: Find a vector parametric equation r(t) for the line through the points P = (4, −3, 4) and Q = (3,…

A:

Q: he vector r(t) is the position vector of a particle at time t. Find the angle between the velocity…

A:

Q: Find a vector equation for the line through the point P = (4, -2, -4) and parallel to the vector vv…

A: P= (4,-2,-4) is a point on the line.  And the line is parallel to v=(4,-1,4)  v is the velocity…

Q: Q#1 (A) Find the reflection through origin and projection onto , axis of the given vector 3 = (-2,1)

A:

Q: Consider the curve = (e', e*, 4t) . r = The component, in the direction of the vector (-1, 1, 2), of…

A: For a curve: r(t), the velocity vector v(t) is calculated using the formula: v(t)=ddtr. The…

Q: Find a vector parametric equation 7(t) for the line through the points P = (3, –4, –1) and Q = (3,…

A: Given points, P=3,-4,-1 Q=3,-3,-1 Find the vector parametric equation from the given conditions.

Q: Find T, N, and B for the curve r(t) = (41, 4t, e' ) at (0,0, 1). Hint: After finding T', plug in the…

A:

Q: Consider the given vector equation. r(t) = (2t - 3, t2 + 3) (a) Find r'(t). r'(t) = (b) Sketch the…

A: Explanation of the answer is as follows

Q: At which point P does the curve r(t)=( 2t³, 21², 3t – 1) givenin vector form have the tangent vector…

A: According to the problem, we have

Q: At which point P does the curve r(t) = ( 21, 4t +1, t) given in vector form have the tangent vector…

A:

Q: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…