A point P(a, 1, -a) is located over a rotating rigid body and its velocity vector is v =[-1, -2, 1]. If the angular velocity is w=[1,0,1], then a is equal to O A. 2 ОВ. 1 ОС. -1 O D. None of these

Q: What is the magnitude of the vector cos 0 i + sin 0j+ 1? 01 O2

A:

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A:

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

A: Solve the following

Q: (a) In a Cartesian plane, if the position vector of a moving particle is given by F = ri+ yj, then…

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

Q: n a Cartesian plane, if the position vector of a moving particle is given by ř = xi + yj, then the x…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: The position of a particle moving in space at time t>=0 is r(t) = 2i + (4 sin t/ 2) j + (3 -…

A:

Q: Given the point D(-4,5,3) and A = ya, + (x + z)z dy, express the D and A in: Kindly answer in vector…

A: Given the point D=-4,5,3 and A→=yax→+x+zzay→. To express D and A→ in: 1. Cartesian Coordinate system…

Q: Given an acceleration vector, initial velocity (uo.Vo). and initial position (xo.Yo). find the…

A: Given that: Acceleration, at=cost,5sint Initial position, x0,y0=3,0 Initial velocity, u0,v0=0,1 To…

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

A:

Q: Two Electric field vectors E1 and E2 are perpendicular to each other; obtain its base  vectors.

A:

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

A: Topic - vectors

Q: 4. If p, 0, z are cylindrical coordinates, show that grad (log p) and grad o are solenoidal vectors.

A: In cyclindrical coordinate systemx=p Cosϕ , y=p Sinϕ , z=zP≥0 , 0≤ϕ<2π , -∞<z<∞dx=dp Cosϕ -…

Q: Question 1 Determine the moment about the origin O of the force F = 2i + 3j – 4k that acts at a…

A:

Q: QUESTION 10 Let r(t)=(1-t2, 5t, 2t3). Find the z-component of the vector r'(4).

A:

Q: Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ,…

A: Consider that: rθ=sin θ, cos θ, cos 3θ at θ=π3. Velocity vector denoted by vθ is vθ=r'θ.  Calculate…

Q: 2. A 6-mC (millicoulomb) positive charge is located in vacuum at P(3,-2,-4), and a 5-uC…

A:

Q: From question 4, determine the vector component of A that is tangential to the spherical surface…

A: Given that A s the tangential to the spherical surface. Where r is 7. Since the surface is…

Q: Given an acceleration vector, initial velocity (uo.vo), and initial position (xo.Yo), find the…

A: Explanation of the answer is as follows

Q: Find the velocity and position vectors of a particle, given its acceleration and initial conditions…

A:

Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

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

A: We will use integration to go toward position fro acceleration

Q: Find the vectors T, N, and B at the given point. r(t) = 7 cos(t), 7 sin(t), 7 ln(cos(t)),    (7, 0,…

A: Obtain the derivative of r(t) as shown below:

Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

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: Find the position vector for a particle with acceleration, initial velocity, and initia a(t) = (2t,…

A:

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

A:

Q: 2. Suppose that the position of a particle is r(t) = (cos(nt), ² sin(nt), t), 0≤t≤ 2n. A. Calculate…

A: Given: The position vector is r→t=2πcosπt,2πsinπt,t and 0≤t≤2π. To find: A) Velocity and…

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

A: We have to find r(t)

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

A: Given,

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(3t), cos(t), sin(t)) when…

A:

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

A:

Q: A person on a hang glider is spiraling upward due to rapidly rising air on a path having po- ition…

A: In this question, the velocity and acceleration vectors are determined from the position vector.

Q: Given an acceleration vector, initial velocity (uo.vo), and initial position (Xo.Yo), find the…

A:

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

A: We have acceleration, initial velocity, and initial position, and if we integrate acceleration with…

Q: If the vector ? has constant magnitude, then show that the vector? and vector dA/dt are…

A: To show that the vector A and the vector dA/dt are perpendicular.Consider A.A = A2cos(0) = K(a…

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A: Let's find.

Q: Let r(t) = (sin 2t ,3t, cos 2t), -n SIST, a) Is speed always constant? b) Show that the velocity and…

A:

Q: If the position vector of a particle P is r(r) (3cos t,5sin7,4 cos t) a) Show that the speed of the…

A:

Q: If the position vector of a moving particle is r(t) = cos(t) î – sin(t) ĵ , then The particle starts…

A: We have to find the starting point for the moving partical.

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

A:

Q: 1. A certain velocity vector V has an X-component, V,, of 12 m/s, and a Y-component, V, of 9 m/s.…

A: To find the magnitude of the velocity vector V.

Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

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

A:

Q: Find the vectors T and N at the given point: r(t) = (cos t, sint, In sin t); (0, 1, 0).

A:

Q: Given an acceleration vector, initial velocity (uo,vo), and initial position (xo,yo), find the…

A:

Q: Let r(t) = (sin(2t), 3t, cos(2t)), t E [-T, "] be the position vector of a particle at time t. (a)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 1. Determine the vector component of A = 3a, + 2ag – 6as tangential to the cone. %3D

A: The vector is A→=3ar+2aθ-6aϕ. Generally, the vectors are shown as sketched below:   Instead of…

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.