Write the vector A = 2z1-xi + yk in cylindrical coordinates.

Q: Find an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

Q: Rotate the vector v = by 0 = 2

A:

Q: Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find the corresponding…

A: Given,

Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

A:

Q: Ps Fnd Parametric equations for the 3. lines through (2,3,0) Perpendliculerr to the Vector uiitzj+3k…

A: First take cross product ie normal vector And then use formula

Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

A:

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x-2y+z = 4.

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Q: What are the vector and parametric equations for ideal projectile motion?

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Q: Express the plane  z = x  in cylindrical and spherical coordinates.

A: it is merely z-x=0.

Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

A:

Q: Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

A: WE know that equation of line through (x1,y1,z1) and parallel to vector ai+bj+ck is

Q: Verify in cylindrical coordinates that V-(ïv)=(V -ū5+ū -Vỹ

A: Given: ∇.u→v→=∇.u→v→+u→.∇v→

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: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 5 sint and 0 = 5t = (Du, + ()…

A: Recall:The velocity is given by      v =r' ur +(rθ') uθandThe accerleration is given by     a…

Q: Evaluate F - dS, where F = and S is the helicoid with vector equation r(и, о) - = 0 < u < 2, 0 < v…

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Q: Give a vector parametric equation for the line that passes through the point (–2, 1, –2), parallel…

A:

Q: 2. Convert the vector A=10ax in the Cartesian Coordinates into a vector expressed in the Cylindrical…

A:

Q: Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

A:

Q: Give a vector parametric equation for the line through the point (4, 2) that is perpendicular to the…

A:

Q: Explain how you can convert from a plane's scalar equation to a vector equation.

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Q: How do you use a point on a plane and a vector normal to the plane to find the equation of the…

A: A vector normal to the plane will be perpendicular to all the vectors lying in the plane. We know…

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: Write the scalar equation of the plane with normal vector = [1, 2, 1)] and passing through the point…

A: here normal vector is  and the given point is

Q: Find an equation for the plane y=3 in cylindrical coordinates

A:

Q: Convert the point (x, y, z) = (1, √3, 2) to cylindrical coordinates.

A: Given: x, y, z=1, 3, 2 To determine: Given coordinates into cylindrical coordinates.

Q: Convert the point from rectangular coordinates to cylindrical coordinates. 11. (0,5,1) 12.…

A:

Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: o v based at the origin.

A: Sketch the vector v = (2, −3) based at P = (1, 4) and the vector v0 equivalent to v based at the…

Q: Find an equation of the plane that passes through the point Po(0,2, – 2) with a normal vector n =…

A: Find an equation of the plane that passes through the point p0 (0,2,-2)with a normal vector…

Q: Verify in cylindrical coordinates that а) b) V. (üv)= (V -ū)ỹ +ū ·Vỹ

A: PART A To prove that : 12∇v→.v→=v→.∇v→+v→×∇×v→ Taking LHS ,…

Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: find The unit Vectors tanent and normal to The ellipse x+2y= 6 at The Point (2,1).

A: Given, ellipse x^2+2y^2=6   point=(2,1)

Q: A vector is 0.888 m long and points in a 205 degree direction. Find the y-component of the vector.

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Q: (b) Convert vector V = 1a, + 4a0 + 3a, from spherical to cartesian at point P = (3, 60°,60°)

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Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

A:

Q: Give a vector parametric equation for the line through the point (-1, –1) that is perpendicular to…

A: We have to write a parametric equation of the line  which is passing through the point (-1, -1)…

Q: How do you find a vector perpendicular to a plane?

A:

Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: Give a vector parametric equation for the line through the point (-2, –2) that is perpendicular to…

A:

Q: Find the component form and magnitude of the vector v. Initial Point Terminal Point (-2, 3) (11,…

A: Given for a vector v,Initial point:(-2,3)Terminal point:(11,-19)

Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Write the scalar equation of the plane with normal vector * - [3, 4, – 1] and passing through the…

A:

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

A:

Q: Plot the point with cylindrical coordinates (2, 27/3, 1)

A: Introduction: The distance from a chosen reference axis, the direction from the axis relative to a…