In each of the following, find the equation of theplane normal to the given vector N and passingthrough the point P0: N = (2, 4, 3)T , P0 = (0, 0, 0)

Q: Find the principle unit normal vector to the curve given below at the specified point. r(t) = ti+…

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Q: Find equations of the following. 2(x - 4)2 + (y - 1)2 + (2 – 6)2 = 10, (5, 3, 8) (a) the tangent…

A: Given that: 2(x-4)2+(y-1)2+(z-6)2=10        and (5, 3, 8)

Q: of the motion of r(t) = . Leave your a

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Q: find T, N, and B for the curve at the indicated point. Hint: After finding T', plug in the specific…

A: The unit tangent vector T, the unit normal vector N and the unit binormal vector B are three…

Q: Q2) Find T N „B of the vectors the curve r(t) = at the point (1, ,1)

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Q: The following parametrizations intersect at the specified point. r1t) = (-5, 1, 2VF + 1), r,6) = (s,…

A: We have to look whether that point lies on both of the paths.

Q: Q2) Find the T „N of the vectors curve r(t) = at the point (1, 1)

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Q: If is a smooth curve given by a vector function r(t) a < t < b and is a constant vector, show…

A: So we have;

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

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Q: 6. Find the unit normal vector to the curve r(t) = (2sint,5t,2 cos t)

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

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Q: '. Given r(t)= (cos 21, sin 21, 31). Find the normal vector N(t), and explain. Then find the…

A: Given,  r(t)=(cos2t,sin2t,3t)             and point p(-1,0,3π/2)

Q: Determine the velocity vector of the given path. c(t) = 9ti + 8t2j + 7t°k

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Q: Given the vector function 7(t) = (t +3, 7t – 5) %3D Calculates the principal normal vector (t)when t…

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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: 7. In this problem, we prove that a straight line is the shortest curve between two points in R. Let…

A: Given - let p,q∈ℝd and r be a curve such that r(t0) =p and r(t1)=q where t0<t1 (a) let r be a…

Q: 2.4 A unit normal vector to the cone 30° is: (a) a, (c) a (b) ag (d) none of these

A: The spherical coordinate system is a special type of coordinate system. The standard form of the…

Q: I can't find the normal component of the acceleration. (aN)

A: For normal component of acceleration:

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: For the space curve in R° graphed below, which you can assume is laying flat on the screen, at time…

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

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: PROBLEM (7): Find the outward drawn unit normal vector n to the surface (i) (x-1)+y?+(z+2)? 9 at the…

A: To find- Find the outward drawn unit normal vector n^ to the surface x - 12 + y2 + z + 22 = 9 at the…

Q: Find equations of the following. 2(x – 7)2 + (y – 5)² + (z – 6)² = 10, (8, 7, 8) %3D - (a) the…

A: Suppose we have given a surface .Then; The equation of tangent plane at   is  . The equation…

Q: Given the vector function. Calculates the principal normal vector N(t) when t=6.9

A: Question- Given the vector function. Calculates the principal normal vector N(t) when t=6.9 ?

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

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Q: 6. d(X, {) seems to depend on the choice of P on { and on the unit normal vector N. Show that if N'…

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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: In Exercises 1 and 2, graph the curves and sketch their velocity and acceleration vectors at the…

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Q: A motion has R++) = (3.8m (347) 2² + (3 cos (3+));²³² + 3 +K A at time + -4 is. A vector dan gend to…

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Q: If the position vector r(t)=e9t i +9sqrt(2)t j + e-9t k, compute the normal component of the…

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Q: 1 8 - Find an equation of the plane containing the Point P (2,1, -1) and having the normal vutor N :…

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Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: Given f(x.y.:)=9x² – 5:-7+xy and Vf = (18x+ y,x,-5). Find a unit %3D normal vector at point P =…

A: As ∇f is the gradient of the surface f , it will point towards the normal vector of the surface.

Q: 3x2 – 4y2 at which the vector 11. Find the points on the graph of z = (3, 2, 2) is normal to the…

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Q: Given the vector T and a sphere with a 2m radius, calculate the circulation of T around the three…

A: Given: Let's calculate the circulation of T along the three pathways designated by segments 1, 2,…

Q: Q2) Find the vectors „N of the curve r(1) = ) at the point (1.1)

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Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

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Q: Compute the unit binormal vector B for the following parameterized curve: F(t) 4 2 3t, 1

A: Given:    r(t) = ⟨ t2/2 , 4-3t , 1 ⟩

Q: 2. Given the space curve .N(77). ² B r(t) = (2 cos 2t, 2 sin 21, 31), find the unit vectors, 4

A: Consider the space curve, r→t=2cos2t , 2sin2t, 3t  To find the unit vectors T→π4 , N→π4 , B→π4 Here…

Q: Find the principal unit normal vector to the given curve at the specified value of the parameter.…

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Q: Given the position vector 7 (t) = of a particle in space at time t. t

A: Given,           The position vector r→t = t+1, t, 1t of a particle in space at time t.

Q: Find the principal unit normal vector N for the curve r(t). (1) = (1² + 3) +(2t – 8) k". %3D

A: Given: r(t)=(t2+3)j+(2t-8)k.

Q: Find the unit tangent, normal and binormal vectors T, N and B for the curve at the point (0, 7, -1).

A: The curve is defined by the vector function rt=sint2,t2,cost2 on the domain [0,∞) To find the unit…

Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: d) Our goal is to find a vector ÂY such that Ax minimizes the distance from b. How does Aâx relate…

A: Let the given system be Ax=b. Assume that the system has no solution. Then we have to find the…

Q: For the space curve in R° graphed below, which vector would be the unit normal vector at time t-1?…

A: We have to find the unit normal vector to the given curve.

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

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Q: (a) Find the position vector of a particle that has the given acceleration and the specified initial…

A: To find the position vector of a particle with given acceleration vector and initial conditions

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.