F G H Trapezoid FGHI is dilated by a scale factor k = 1/2 with center of dilation at point F and then translated along the vector (4, –3) .What are the coordinates of the FIRST image?

Q: 9. DABCD is a convex quadrilateral. Let P, Q, R, S be centers of the squares drawn (externally to…

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Q: Find the positive t when the vector r(t) = (4t, 4ť, 5t² – 6) is perpendicular to r' (t). -

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Q: Find the unit vector in the same direction as the vector u = [8, –7].

A: When you divide a vector by its magnitude you get an unit vector along its direction.

Q: 5. a) What is the orthogonal projection ŷ, of y = 1 = ( ² ) U = and the origin? -3 9 onto the line…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: The given vector is r→t=5t sint + 5costi^+5t cost + 5sintj^. To find: (a) unit tangent curve of the…

Q: 2. Let P be the point (-3, 5, 4). (b) Find the distance from the point P to the yz-plane. Find the…

A: Let P be the point .(a) To find the distance from point P to the yz-plane.(b) To find the distance…

Q: 3. (Sinx, Sinzx, 4. for the given vectors find the value of normalize W+V π = (1, 1, 3) V = (3, 1,…

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Q: Describe the curve represented by the vector-valued function r (t) = (2 cos t) i +tj + (2sin t) k…

A: Given: r→(t) =2costi→+tj→+2sintk→. x=2costy=tz=2sint Then, x2=costz2=sint

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

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Q: 8. The magnitude of force F is 450 lb. Express F in Cartesian vector form. y, ft 030° A(4,-2) -x, ft

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Q: Look at attached image, thank you

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Q: A velocity vector of variable magnitude of an object can have a constant direction. O True False

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Q: Q4\A: Find area of zone bounded by curves x = y? 2y = x-3 B: Find area of triangle whose vectors…

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Q: d. In which direction is the instantaneous rate of change the maximum from (1,0)? What is the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Given the vector-valued functions u(t)= esti+e-¹ + 2tk v(t) = 2ti - 3t² + 3k d find (u(t) v(t)) when…

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Q: Identify the direction from graph of functions given below: vector i) r = i(2 cos 21)+ j(2sin 2r) ;…

A: Given, r→=i^(2cos2t)+j^(2sin2t) Identify the direction vector, From the given position vector,…

Q: On a metal plate in the shape of a rectangle, the temperature at a point (x,y) is given by; 100 3x²…

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Q: Part B please g(x,y,z)=x^2+y^2+(z-3)^2

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Q: (3.) (a.) (Circle the correct choice) Which of the following vector functions describes a circle of…

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Q: "Velocity" Vector or Scalar?

A: A mathematical quantity (physical ) is an amount or a number. The physical quantity can be any…

Q: (c) Use vector methods to find the point P on the circle (x - 5)² + (y-4)² = 4 which is closest to…

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Q: An object moves with the acceleration vector ä(t) = with initial ity vector Po= and initial position…

A: Given acceleration of an object after time t is a→t=-2.i⏜+j^+3k^ Let the position vector of the…

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.