Consider the plane: 2.x + 2y + z = 3 Find a unit normal vector.

Q: Find the principal unit normal vector N of the curve: r(t)=(7tsint+7cost)i+(7tcost-7sint)k

A: The given curve is r→t=7tsint+7costi^+7tcost-7sintk^ We have to find the principal unit normal…

Q: find a vector normal to the plane with the given equation. x − z = 0

A: Given: Plane: x-z=0 To Find: A vector normal to the given plane

Q: Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

A: Consider the equation of the plane passing through a general point Po and with normal vector n.

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

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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: What is the normal vector, n for S is a surface of x +y² +z² = 36 in the first octant? %3D

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Q: Calculate fu-2)- N ds where C is circle of radius 3 centered at the origin and N is an outward…

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Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

Q: Find a unit vector n that is normal to the surface 4z? – 2x* – 3y = 14 at P = (1,2, 4) that points…

A: To Determine: Find the unit normal n that is normal to the surface at p(1,2,4) that points in the…

Q: The principal unit normal vector on the curve r(t)= (2 sint,2cost) %3D (a) always points directly…

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: For the curve given by the vvf r(t) = ti + 2t²j+t³k, find the unit tangent T(t), principal normal…

A: I have appended the formula used in the solution part of the question

Q: Find the unit tangent vector T, the principal unit normal vector N, and the unit binormal vector B…

A: Consider the curve     Ct: rt =cost,sint,t (i) unit tangent vector                  The unit tangent…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given two surfaces Z =   x2 + y2  and  plane z = 9 + y  We have to find vector function   r (t) We…

Q: (b) Verify your answer in (a) using Stokes' theorem, where the normal vector to the surface has a…

A: We have to apply Stoke's theorem.

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

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Q: 19. Suppose that the normal unit vector N of a surface S at z =f (x,y) is determined, how does the…

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Q: A particle is moving along the curve whose position vector is given: R(t) = (cost + tsint)i + %3D…

A: R(t)→=cost+t sinti+sint-t costj+4kFind the unit normal vectorSome…

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: find an equation of the normal plane through the point t=pi/3.  r(t) = 2sin(t)i+. 4cos(t)j +tk

A: Given curve is r(t)=2sin(t)i+4cos(t)j+tkr'(t)=2cos(t)i-4sin(t)j+k At t=pi/3…

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the…

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Q: Find a vector parametrization for the intersection of the plane x + y+z = 3 and the cylinder x² + z2…

A: solution given below..

Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: Find the tangential and normal components of acceleration for the position vector given by r(t) =…

A: Given: rt=3ti-tj+t2k

Q: A partidle is moving along the curve whose position vector is given: R(t) = (cost + tsint)i + (sint…

A: As we know that the simple form of the position vector is:   r→=xi+yj+zk   From the given problem:…

Q: Find the tangential and normal components of the acceleration vector. r(t) = ti + j + 4tk 4r V 17+42…

A: Given:- r(t) = ti + t2 j +4k  To find:-  Tangential and normal components of acceleration vector

Q: H.W: find vector parallel to the line of intersection between two planes. 1) x+y+z=1 and x+y= 2.

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Q: find a normal vector to the plane.

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Q: 19. Suppose that the normal unit vector N of a surface S at z = f(x, y) is determined, how does the…

A: Note: As company policy, we solve first question only. Please resubmit the rest of the questions in…

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r=7 e ao and = 3 dt V = +

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Q: Find the value of a at which the plane curve traced out by the vector function E + bt> is not…

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Q: The unit normal vector to the surface x'y + 2xz? = 8 at the point %3D (1,0, 2) is

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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: A particle is moving along the curve whose position vector is given: R(t) = (cost + tsint)i + (sint…

A:

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: e the electric flux through a paraboloid z = x² + y² – 16 that lies . It is oriented by an outward…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

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Q: Evaluate Vx(3xj) •n do where S is the hemisphere x + y² +z? = 4, z20. Use the normal vectors pointed…

A: Please see the explanation below

Q: Find the principal unit normal vector for the helix r(t) = 2 cos ti + 2 sin tj + tk.

A: Given, r(t)=2 cost i+2 sint j+t k

Q: Find a vector n normal to the plane with the equation x+6y + 4z = -10. n= 00> (1₂)

A: Concept: The equation of the plane is written as: ax-x0+b(y-y0)+c(z-z0)=0 or ax+by+cz=d Here the…

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

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Q: Find the unit normal vector to the surface f(x,y) = y² – 4xy at (1,2). (a) i (b)- i (c) 8 i+4j (d)0…

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Q: Find a unit normal vector to the surface f(x, y, z) 0 at the point P(4, – 5, – 5) for the function…

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Q: Find a unit normal vector to the surface f(x,

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Q: Find the tangential and normal components of the acceleration vector. r(t) = 4(3tt³)i + 12t²j aT an…

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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: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.