A particle starts moving from (- 4, 2, 5) so that its initial velocity is 5 î -3 ĵ – 2k and its acceleration vector is a(t) = (2 t+3) î + (4 t – 1) ĵ +6k then after one minute, the particle will be at the point: 1) (용,-풍, 1) ,1) 2) ( 5, 3, 6 ) 6 6 3) (, -4) 4) (풍,-8,6) 17 17 5 6. 6

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

A:

Q: If a particle moves in the xy-plane so that at time t > 0 its position vector is (In (t2 + 2t) ,…

A: As we know that the expression for the velocity is; v=dstdt Given position vector is:…

Q: 10) Find a unit vector in the direction that f (x, y, z)= 2x² +6xy² – xz' increases most rapidly at…

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Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A:

Q: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

Q: find a vector parametrization for the line with thegiven description.Passes through P = (1, 2, −8),…

A: Find a vector parametrization for the line with the given description. Passes through P = (1, 2,…

Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: 3. Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

A:

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

A: We have

Q: 5. Suppose a particle is moving along a smooth path r(t) with constant speed. If a(t) + 0, show that…

A: Two vectors is perpendicular if their dot product is zero.

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: give the position vectors of particles moving alongvarious curves in the xy-plane. In each case,…

A:

Q: find a vector parametrization for the line with thegiven description. Passes through O and (4, 1, 1)

A: To findvector parametrization passes through O and (4,1,1)

Q: Find the velocity vector in terms of u, and ue- T=2 cos 2t and 0= 4t %3D O A. v= (4 sin 2t)u, + (8…

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Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: Show that if a particle moves with constant speed, then the velocity and acceleration vectors are…

A:

Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

A:

Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1)…

A: To find the vector parameterization for the line that passes through the point (1, 1, 1) and…

Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

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Q: It is known that the acceleration vector for a particle is given by A(t) = 4j + 2tk. Determine the…

A: We need to determine vector equation of curve traced.

Q: If the vector K az+Lay+ Ma, shows the maximum increase rate and direction of the scalar V at point…

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Q: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

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Q: Find a unit vector in the direction in which f (x, y, z) = 3x³z² + 3y°z + 24z – 4 increases most…

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Q: When body is an equilibrium ,the net force is vanish ulgn O İhi O

A: when body is an equilibrium the net force is vanish

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

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Q: 'Two particles moving with constant velocity are described by the position vectors: P = Po + vt, s =…

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Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

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Q: 2. If a particle moves in the xy-plane so that at any time t > 0, its position vector is (In(r² +…

A: Solution-

Q: Find the Directional Derivabive of Pary,2)= x-yz'+ at the point CI, -2, 0) in the direcbion of…

A: A scalar function is a rule to associate a number to a particular point in space. The directional…

Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 - cos θ) and dθ/dt = 3

A: Velocity is defined as the rate of displacement. Acceleration is known as the rate of change in…

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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Q: The position of a particle moving in the xy-plane is given by the vector (4t, y(2t)), where y is a…

A:

Q: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

A: position vector of a particle in the xy-plane is given by < t^2+1, ln(2t+3) > for all t>=0

Q: Find the work done in moving a particle from point P(- 5, 0, 2) to Q(3, - 1, 4) if the magnitude and…

A: To find the work done in moving a particle from point P-5,0,2 to Q3,-1,4 Also the magnitude and…

Q: Two blocks, with masses 4.00 kg and 8.00 kg, are connected by a string and slide down a…

A: To calculate the acceleration.

Q: Find a nonzero vector u with initial point P(2,-3,6) such that: (a) u has the same direction as v =…

A: Find a nonzero vector u with initial point P(2,-3,6) such that: (a) u has the same direction as v =…

Q: In a horse race, horse 2 passes horse 1 at point A, where the two velocities are v₂ = m 7™ and v₁ =…

A: To determine the distance from point A to B and the position of horse1 relative to horse 2 when…

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

A: The line integral ∫CF·dr involves the integration over a specific path. In this problem, the…

Q: Prove that the vector T'(t) = 0 for moving in a straight line

A: Note that, the object's path is rt=xti+ytj. yt=mxt+b, where m and b are constant. It is known that,…

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 +y? = 200 and y? + z2 =…

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Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

A:

Q: Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1,…

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Q: Find two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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Q: 4. If a particle moves in the xy-plane so that at time t its position vector is sin 31 ,3r2 find the…

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Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to <2,1>

Q: Find a nonzero vector parallel to the line of intersection of the two planes 4y – 3x +3z = -2 and z…

A: Answer

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.