(a) Ã(x, y, z) = ë %3D (d) Ã(p, ø, 2) = ë, (g) Ã(r, 0, 4) = ë, %3D (j) Ã(x, y, z) = x2 + y?

Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

Q: (A) Find the vector that is Normal to: A = 2i + 3j +k and such that it is lies in the plane…

A:

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (1, −1), v = (1, 1)

A:

Q: Let vi, ..., v be vectors, and suppose that a point mass of m,, ..., m, is located at the tip of…

A: Given: u1=-1, 0, 2   and     m1=2u2=2, 1, -3   and     m2=1u3=0, 4, 3       and     m3=4u4=5, 2, 0…

Q: Consider the vector v = (x, 2) in R2. If you rotate the vector by 90-degrees counter-clockwise, then…

A:

Q: Express in cylindrical components: (a) the vector from C(3, 2, -7) to D(-1, -4, 2); (b) a unit…

A:

Q: Find the angle between the vectors u = (1, −1) and v = (0, 1).

A: Given query is to find the angle between the vectors.

Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: A vector of 2 unit length parallel to vector 2i + 2j+k is:

A: We know a vector consists of magnitude and direction as we have to find the direction parallel to…

Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

A:

Q: The unit vector perpendicular to the vectors n1= i-j+3k ,n2=2i+j+3k is a vector?

A:

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. 1 Find the unit vector…

A: Given, X = -i + 3j  and Y = 4i -2j + 2k

Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w - x -y+ 3z 0, %3D…

A:

Q: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

A: The vectors v and w are in the x-z plane. The cross product of both vectors will yield a vector…

Q: Find a unit vector orthogonal to both u and v.u = i − 2j + 2kv = 2i − j − 2k

A: Given  u = i - 2j +2k = < 1, -2, 2 >v = 2i - j - 2k = < 2, -1, -2 >

Q: 6. For the vectors ü = (4, 3) and i= (-2, 3), caleulate the following quantities. (a) la+ 레 (b) la+…

A:

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a…

A:

Q: Find a unit vector normal to the plane containing v=i+3j-2k and w=-2i+j+3k.

A: There are two types of quantities that exist in nature, one is scalar quantity and the other one is…

Q: Q. For the Spheri cal polas Coozdinates (r0,d), prove that their unit vectors mutually orthogonal?…

A:

Q: Find a unit vector orthogonal to A in the plane of B and C if A = 2i - j + k, B = i + 2j + k, and C…

A: The given details are as follows.

Q: Two vectors of magnitudes A=3 and B=3v2 are lying on the xy plane as shown in the figure. What is…

A:

Q: Consider the vector v = (2, y) in R?. If you rotate the vector by 90-degrees counter-clockwise, then…

A: Given,   v=2,y   in ℝ2.

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a –…

A:

Q: Given the 3-dimensional vectors: A = (xy)i + (2yz)j +(3xz)k B = (yz)i + (2xz)j +(3xy)k Determine the…

A: Here given vectors as A=xyi+2yzj+3xzkB=yzi+2xzj+3xyk

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A:

Q: The volume of parallelepiped determined by the vectors u = 2i – k, v = 2j – 3k and .= w = i + j+k is…

A: We use the definition of the volume of a parallelopiped determined by the vectors a, b and c to find…

Q: 2. If A is the position vector of the point p-(x,y,z) and A=A. And ifr is the radius of the point in…

A: We apply the cross product to find the given function and simplification needed.

Q: Express in cylindrical components: (a) the vector from C(3, 2, –7) to D(-1, –4,2); (b) a unit vector…

A:

Q: 3. Find two unit vectors orthogonal to both j − k and i + j

A: We will find the two unit vectors orthogonal to j-k and I+j as following.

Q: Find the angle θ between the two vectors.u = (1, −1), v = (0, 1)

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: Find the normal unit vector perpendicular on à and B for A = 2i+3j-k and B=-j+2k %3D

A: To find the normal unit vector perpendicular to A and B

Q: (g) Ã(r, 0, ø) = ẽo (h) Ā(x, y, 2) = yë, - xẽy (i) Ã(x, y, 2) = %3D x2 + y?

A: According to company policy we solve only 3 subparts of a given problem so please ask rest parts in…

Q: Find a unit Vector orthogonal to both vectors: U =21 +5j-K and V=i+3j-2K.

A: We can find the unit vector as below

Q: Give the unit vector in spherical coordinates that extends from M(5,1,2) to N(2,4,6).

A:

Q: 10 Give an expression of a vector, B = aR + R cosoae + a, in Cartesian and R cylindrical…

A:

Q: 2) With respect to the origin 0, the position vectors of points A, B, Cand D are given by OA = 1 OB…

A:

Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

Q: 3. Find the angles between the vectors: u = 2i + j, v = i + 2j – k а. -

A:

Q: Find unit vectors Parallel to the YZ Plaane and PerPendicular to the Vector V = 51-j+2k ?

A:

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 unit vectors of Cartesian Ox,X,x3, cylindrical Opøx, and spherical Oroø coordinate systems are…

A: Given that x1⏞,x2⏞,x3⏞, ρ^,ϕ^,x3^ and r^,θ^,ϕ^ are unit vectors of Cartesian, cylindrical and…

Q: Find a unit vector orthogonal to both u and v. u = i + 2j + 2k v = 2i +j – 2k

A:

Q: Convert the following vectors to their equivalent vectors in cylindrical and spherical coordinate…

A: The components of the spherical vector are r,θ,ϕ Which are related as r=x2+y2+z2…

Q: Given a vector à = 2êp + ê - 4êz, convert A into: П a. Cartesian coordinates at point (3, 2)…

A:

Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

A:

Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: First take gradient and magnitude of gradient

Cylindrical Coordinate System

The distance from a selected reference axis, the direction from the axis relative to a selected reference direction, and also the distance from a selected reference plane perpendicular to the axis area unit, all accustom outline purpose positions in a cylindrical reference frame. Counting that the aspect of the reference plane faces the purpose, the latter distance is expressed as a positive or negative variety.