(A) Aunit vector u in the direction of the vector P( 2,0, 2) to Q( 4,2,0) (B) The vector projection of u = i +j+k on to v 5 j- 3k (C) The volume of parallelepiped determined by vectors u = i+j-2k v= - i - k w = 2i +4j - 2 k

Q: Find a vector parameterization of the plane 5x−4y−1z=18

A: By using prametrization

Q: 41. The cone z = /x² + y² and the plane z = 1 + y

A: Solution: The objective is to find a vector function that represents the curve of intersection of…

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A:

Q: 36. A plane has equation z = 5x – 2y+7. (a) Find a value of à making the vector di +j +0.5k normal…

A: we have to find

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A:

Q: Heat flux Let D be a solid heat-conducting cube formed by the planes x = 0, x = 1, y = 0, y = 1, z =…

A: Draw the cube formed by the planes and Plot the coordinate of point Q. Observe the figure carefully.

Q: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z)…

A: The position vector,

Q: F. Use Green's Theorem to calculate the circulation in the presence of F(-y², x) around the…

A:

Q: 10. Consider the plane P given by r + y – 3z = 0. (a) Find the projection of the vector (2, 1, 0)…

A: Given plane : x+y-3z=0  Projection of A along B is A.B/|B|

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A:

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A:

Q: 4. Calculate the vectors A and C curves given below with l Ádl Note: For closed curves, unless the…

A: answer is 2*pi

Q: 3. A scalar equation of the plane with normal vector = [0, -1, 3] and passing through the - point…

A: Topic = Geometry Correct option = A

Q: 10. Consider the plane P given by a + y-3z 0. (a) Find the projection of the vector (2, 1, 0) onto…

A: Given,Equation of plane P - x+y-3z=0 To Find: Projection of vector (2, 1, 0) onto the plane P

Q: -2 Let L be the line in R' that consists of all scalar multiples of the vector Find the orthogonal…

A:

Q: The temperature is T degrees at any point (x, y, z) in three-dimensional space and T(x,y, z) = 1/(x²…

A:

Q: Write the equation of the plane with normal vector n=5jn=5j passing through the point…

A: Given,

Q: 5 Given a vector equation of the plane 7 = [0, 0, 5] + s[0, 1, – 2] + [-1, 3, 0] determine its…

A:

Q: Vector Field: F(x,y) = (xv, 3x, – 2y) and Surface: z = 4 - x - 3 y? Use the normal vector formula to…

A: Given surface z=4-x-3y2

Q: Q4. State Green's theorem for the plane. Verify Green's theorem in the plane for O (3x2 – 8y2)dx +…

A:

Q: Find a vector function that represents the curve of intersection of the cylinder x^2 +y^2 =1 and the…

A:

Q: (2): Consider the curvilinear coordinate system defined by 2 X = uj-12, y = 2 u, u2, z = u3 Show…

A: We'll answer the first question since the exact one was specified.  Please submit a new question…

Q: cise 1.10. (a). Let V = R² = {(x,y)| x,y 2 0} with usual addition and scalar multiplication. Is it a…

A: Multiple:   Let , V = ℝ2 = x , y | x , y ≥ 0. We need to show that , V is a vector space or not. We…

Q: Bendixson’s criterion The streamlines of a planar fluid floware the smooth curves traced by the…

A: Solution Given  The streamlines of a planar fluid floware the smooth curves traced by the fluid’s…

Q: Vector A =x-a, + 2y · a, – z · az, please: 1. Express A in cylindrical and spherical coordinate 2.…

A: Given: A=x·ax+2y·ay-z·az To express: A in cylindrical and spherical coordinate. To evaluate: A at…

Q: Sketch the vector and scalar fields. Describe the nature of vector fields Find also Curl and…

A: given: p=7 for part (i) to (v): i)     F=xi-yjii)    G=xi-yjiii)   H=cosx+yi+sinx-yjiv)   f=4x-3y+pz…

Q: 96. An ant is at the point (1, 1, 3) on the surface of a bowl with equation z = x² + 2y², where x…

A:

Q: H-pz cos At point (1, x/3, 0), find (a) H a, (b) HX & (c) The vector component of H normal to…

A: As per bartleby guideline for more than three sub parts asked only first three are to be answered…

Q: 3, Four- vectors and Yy in the Schwarzschild space time Ne giver as %3D a) Find the covariant vector…

A: From the given information. X∝=1010Y∝=0101

Q: 43. Volume of a Parallelepiped Find the volume of the parallel- epiped determined by the vectors u =…

A: Rewrite the given vectors. u=2i−j=2i−j+0kv=2j+k=0i+2j+kw=3i+j−k

Q: 6. (a) Show that the curve represented by the vector function F(t) = (5t, 3t – 4, 2t² – 6) is at the…

A:

Q: 7. Consider the plane in R3 defined by 3x + y- 4z 12. a. Give a normal vector for this plane. b.…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: (1) The unit vector in the direction of the vector 37+ 4k is (2) The dot product (-2,1,3) (5,4, 3) =…

A: As per company's guidelines, I can answer only one question. Repost the question to know rest.

Q: 42-46 Find a vector function that represents the curve of intersection of the two surfaces. 42. The…

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Q: 8. All parts of this problem refer to the parametric surface S given by the vector func- tion r(u,…

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Q: The acceleration of a moving particle in space is given by the vector function a (t) = 3t2 i + 4t +…

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Q: A force F of 6 units acts through the point P = (2, 3, 1) in the direction of the vector (4, 1, 2).…

A: the moment formula M= r×F here r = vector PQ r =  OQ→-OP→ = (-1,-1,0) And the F vector is 6 times…

Q: a) A three dimensional motion of an object is given by the vector function UTM r(t) = 4 cos t i+…

A:

Q: Evaluate the integral of vector function F(x,y) = x - y where the boundary curve is the triangle…

A: Given: Fx,y=xi-yj we need to find ∫F·dr, where r=xi+yj over the triangle formed by points…

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A: Given, fx,y,z=x2yz at Point P-1,2,16 The directional derivative is used to determine the direction…

Q: Let x, y € R. Given that the vectors (xi - y, y + x, -yi) and (1 + ix, 0, x - -y) have unit…

A: let x,y∈ℝ , given that the vectors xi-y , y+x , -yi and 1+ix , 0 , x-y have unit magnitude , then…

Q: 2. 3. 3. t.5-2 show that O vector Cusis Perpendicular to the vectors LU) und LW) 2 vector Cs…

A: Two vectors a→ and b→ are said to be perpendicular if their dot product that is a→·b→ is equal to 0.…

Q: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z)…

A:

Q: n equation of the plane with normal vector n= (-3, –3, –9) passing through the point (-4, 7, –9) in…

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Q: Indicate whether the statement is true or false. 1. There is only one scalar equation for a given…

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Q: Exercice 1 Given the vectors u ( 1;2;3) and v(-1;–1;2). Determine the vector w ( 7; y;z ) orthogonal…

A:

Q: Two vector fields are F = -10ax + 20x(y – 1) ay and G = 2x²y ax – 4ay + Zzaz. For th point P(2, 3,…

A: Given- Two vector fields are F = -10ax + 20xy - 1 ay and G = 2x2y ax - 4ay + zaz To find- For the…