10 Give an expression of a vector, B = aR + R cosoae + a, in Cartesian and R cylindrical coordinates. Calculate B (-3, 4, 0) and B (5,", -2).

Q: 4. Find a unit vector that is perpendicular to (5,6).

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Q: 1 of the unit vector u =- +!= j. 2/2 2/2

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Q: The value of the chiral vector of SWNTs if the n=8 , m=6 and the first vector length equal n/2+1 and…

A: Given that m=6,n=8to find the chiral vector of SWNT.  As we know that, the chiral vector c can be…

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

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Q: 4. If p, 0, z are cylindrical coordinates, show that grad (log p) and grad o are solenoidal vectors.

A: In cyclindrical coordinate systemx=p Cosϕ , y=p Sinϕ , z=zP≥0 , 0≤ϕ<2π , -∞<z<∞dx=dp Cosϕ -…

Q: 2. A 6-mC (millicoulomb) positive charge is located in vacuum at P(3,-2,-4), and a 5-uC…

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

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Q: Find volume V(S) of the parallelepiped S in R3 determined by the (3,4,1); v3 following vectors: vị =…

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Q: 2 3 Let u and v %3D . Find the length of 2u and the length of -v. - Find the distance between u and…

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Q: 4. Find a unit vector in the same direction as the vector 8i- j+ 4k.

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Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: nd the flux of the vector v=⟨x,y,z⟩ along the surface of the right tetrahedron below.

A: Flux of the vector

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: c)) find a unit vector perpendicular to plane POR. P(1, -1, 2), Q(2, 0, – 1), R(0, 2, 1) . P(1, 1,…

A: We have to find the unit vector perpendicular to the plane according to the given information

Q: 1 u (-y°i +x rmal vector to

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Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Given the cylindrical coordinates: A(5,30°, 6) and B(7, 60°, -3) E. Determine the vector that…

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Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

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

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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: Q/ find all unit vectors parallel to the yz plane and perpendicular to the vector V= 5i - j + 2k ?

A: Given,   A vector V= 5i - j + 2k.

Q: 2 Let u = = 1 (i) Find the angle between u and v. (ii) Find a vector w of length 2 in the direction…

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Q: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

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Q: ransform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates

A: For the vector given by xi+yj+zk. For the cartesian coordinates P(x,y,z),the corresponding…

Q: 4. A vector normal to the paraboloid z = (x² + y*)/2 is (a) (х, у.1). (b) (2x,2y,–1). (e) (-х,-у.1).

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Q: Calculate the coordinates of the vector w obtained by rotating anticlockwise the vector v= [0, -1,…

A: When a coordinate is being rotated along the direction of a vector by a certain angle, the new…

Q: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

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Q: Show that the vectors a = 3i+ 4j and b = 4i - 3j are perpendicular. A smooth sphere A of mass 2m…

A: Consider the given: a→=3i^+4j^b→=4i^-3j^ mass M of sphere A=2m velocity of sphere A of mass…

Q: what are the components of a vector? what if the initial point is not (0,0)? given a vector v and a…

A: A scalar is a real number. A scaler is a single, independent number.  A vector is a ordered…

Q: Find the equation for the plane through the point Po= (9,2.5) and normal to the vector n= 31 + 10j +…

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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…

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Q: Find all unit vectors parallel to the JZ plane and perpendicular to the vector V = 5i -j + 2K %3D

A: A vector is parallel to yz-plane and perpendicular to the vector v, we have to find the unit…

Q: Qy: In VĘ CR) find all vectors which are orthegonal to u=(1,-2, 3) uut corath

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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: 5. Find a nonzero vector orthogonal to the plane through the points P(1,0, 1), Q(-2, 1, 3), and R(4,…

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

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

A: *concept:- cylindrical co-ordinate = (x, y, z).

Q: Find the vector of velocity which has a speed of (90m/sec) and parallel to the vector joining the…

A: Let Vector a is parallel to vector b then vector a = K Bn Where K is some constant and Bn is the…

Q: Find a vector parametrization for the line with the given description. Perpendicular to the…

A: Given points are (0,0,8). The equation of yz-plane is given by ⇒x=0 Therefore, the normal vector is…

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: 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: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: Find a unit vector in the xy plane that is orthogonal 2 to 4 6

A: We have to find the unit vector.

Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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Q: The vector u = i - 2j + 2k is positioned at a point P in space with coordinates: (x, y, 2) = (1, 2,…

A: Given:    The vector u = i-2j+2k is position at a point P in space with coordinates: (x, y, z) = (1,…