Let the position vector bc RCE): the unit tangent Compute vector T(E).

Q: Sketch the plane curve represented by the vector valued function, and give the orientation of the…

A: To Sketch the plane curve represented by the vector valued function Give the orientation of the…

Q: Find the ualt noima vector fol for Rhe Lvector valuhed P(4)=t t? and sketch the durve the vector…

A: To Find:

Q: Find the arc length of the space curve given by the vector equation r(1) = (- 9t + 16) + (-9² +…

A:

Q: Evaluate | F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 4, 0 < v…

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Q: Find the acceleration vector for the position vector r(t) = (sin(5t), 6t", e "). x component = y…

A:

Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: Sketch the space curve represented by the vectorvalued function                  r(t) = ti + (2t −…

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Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

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Q: Graph the vector function r(t) = (cos t)i + (sin t)j + t k.

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Q: cos(ti) + t^3j and the initial position R(0) = i − 2j.

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Q: Find the arc length of the vector equation, r(t)=ti+8sintj+8costk for 0<t< 47.

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Q: Show that, û . ûm = 0, Use only the fact that û,is a unit vector. Interpret this result.

A: Here we need to prove that dot product of a unit vector and its derivative is zero. Here we use the…

Q: Let h ( x , y ) = ln ⁡ ( ( x + y ) 2 ) . If you are at the point ( e , e ) what unit vector makes D…

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Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=&lt;4, -5, 7&gt; onto the vector…

Q: Find the acceleration vector for the position vector r(t) = (sin(11t), 4t°, e-11t). x component = y…

A: Given : rt → = sin11t, 4t8, e-11t

Q: Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 3, 0 < v < T…

A: Given that, F¯=y,-x,z5 and ru,v=u cos v, u sin v, v where 0≤u≤3 and 0≤v≤π. Find ru×rv as follows.…

Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

A:

Q: Evaluate :// F. d5 , where F = and S is the helicoid with vector equation r(u, v) upward…

A:

Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: Consider an object moving according to the function from position r(t) = acoswt i + asenwt j. To…

A: As per the question we have to find the tangential and normal vector components of the path defined…

Q: Let b = i + j − k. Find (algebraically) the unit vector in the direction opposite to b.

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Q: Suppose that C has length 5. What is the value of F. dr if: (a) F(P) is normal to C at all points P…

A: Given: Length of C is 5. (a) F(P) is normal to C at all points P on C. ∫CF→·dr→=∫CFdrcos90°=0…

Q: Sketch the curve represented by the vector-valued function                               r(t) = ⟨…

A: Given  r(t) = ⟨ cos t, sin t ⟩

Q: Evaluate F· dS , where F = and S is the helicoid with vector equation r(u, v) upward orientation.…

A:

Q: The acceleration vector points in the direction of motion. O True O False

A: If acceleration is positive then the acceleration vector points in the direction of motion.  But if…

Q: Evaluate || F . d5, where F = and S is the helicoid with vector equation r(u, v) = Is 0 < u < 4, 0…

A: The solution are next step

Q: What is the unit tangent vector to the curve r(t) = ti + t²j when t = 1. Select one: (i+2j) O (i+…

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Q: Find the vector r' (to); then sketch the graph of r (t) in 2-space and draw the tangent vector r'…

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Q: Consider the vector functionrit)-(1, 2t, t"), Find the unit tangent vector T(t) when t

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Q: Dz: tow ord the find the unit vector Curve y =x? at

A: Find the unit vector towards the curve y = x2 at x= 1: r→t=xti^+ytj^y=x2:Let xt=t  and…

Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS

Q: The divergence of a vector D for rectangular coordinate is equal to [1/p / dp (pDp)] + [1/p Dø/dø]+…

A: We have to find divergence in rectangular coordinate

Q: The magnitude of the torque t developed by applying a force F at a point with position vector r at…

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Q: Find the unit tangent vector at the indicated point of the vector function r(t) = e3tk T(pi/2) = %3D…

A: Here the given vector is  r→(t)=e3t cos(t) i+e3t sin(t) j+e3t kr→(t)=e3t cos(t) , e3t sin(t)  , e3t…

Q: Find the unit tangent vector at the indicated point of the vector function r(t) = e3t cos fi+ et sin…

A: We use the following formula to find the unit tangent vector T(t)=V(t)/|V(t)|

Q: Sketch the curve whose vector equation is r(t) =

A: given rt=&lt;tcost,tsin,t&gt;

Q: Evaluate F. dS, where F = and S is the helicoid with vector equation r(и, v) with upward…

A:

Q: Given r(t) 12ti + 5cos ti + 5 sintk, find the unit binormal vector and torsi =

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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: Sketch the curve with the vector equation ř(t) = (sin t, t). Indicate with an arrow the direction in…

A:

Q: Sketch the curve of the vector function r(f) = ti +4costj, and indicate the orientation of the…

A: We have to sketch the curve of the vector function rt=ti+4costj, and to indicate the orientation of…

Q: Evaluate /| F · dS , where F = and S is the helicoid with vector equation S r(u, v) 0<u < 1, 0 <…

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Q: The angular velocity w is a.. quantity. vector conserved fundamental

A: Third option is correct.

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

A: The given vector equation is

Q: Give a vector description of the midpoint M of a line segment AB→.

A: GivenLine segment AB→To find vector description of midpoint of AB

Q: Evaluate F. dS, where F = and S is the helicoid with vector equation r(u, v) = 0< u < 2, 0 < v <…

A:

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.