3 Among all unit vectors u = y in R', find the one for which the sum x + 8y+ 4z is minimal.

Q: 7. Find an initial point P of a nonzero vector u = PQ with ter- minal point Q(3, 0, –5) and such…

A: We have to find an initial point P of a non zero vector u = PQ→,  with terminal point Q(3, 0, -5)…

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

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Q: Find a unit vector n that is normal to the surface 4z - 2x - 3y = 14 at P = (1,2,4) that points in…

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Q: find a vector parametrization for the line with thegiven description.Passes through P = (1, 2, −8),…

A: Find a vector parametrization for the line with the given description. Passes through P = (1, 2,…

Q: A. If x and y are orthonormal vectors, then find the valne of x+ yl? - |x-yl

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Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1) and…

A: The vector parametrization is:                                       r(t) = r0 + tv = x0,y0,z0 +…

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: 5- The value of the chiral vector of SWNTS if the n=8, m=6 and the first vector length equal to +1…

A: n=8 m=6

Q: An elastic string is stretched between two points 40 cm apart. Its center point is displaced 1.5 cm…

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Q: Obtain a vector orthonormal to the vectors i−j  and (1, 0, 1)

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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: Find the velocity vector in terms of u, and ue- T=2 cos 2t and 0= 4t %3D O A. v= (4 sin 2t)u, + (8…

A:

Q: XII. Show that the dual vector of the antisymmetric part of the dyadic (1 2 3) A = 4 2 1 1 1 1) is…

A:

Q: Find an equation of the plane through the point (4, 5, 1) and with normal vector 6i + j - k. Show…

A: The plane passing through a point A(a) with the normal vector n is given by: r·n=a·n where,…

Q: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

Q: 1. Let (r,0,ø) be spherical co-ordinates. Show that the unit vectors in spherical co- ordinates are…

A: Below is the step wise detailed proof :

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

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Q: A. If x and y are orthonormal vectors, then find the value of x+ yll- x-yll

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Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1)…

A: To find the vector parameterization for the line that passes through the point (1, 1, 1) and…

Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

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Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

A:

Q: why you write: s=0, t=0 s=1, t=1  instead of using cross product imediately between 2 vectors…

A: The vectors (1, 0, 1) and (1, -1, 0) are direction or orientation vectors. The cross product of…

Q: Find basis for the set of vectors in R2on the line y=nx. where n is last digit of your arid number.…

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Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

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Q: 18 as a linear combination of = 8 Express the vector i and j =

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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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: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

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Q: ☺ Find the unit fenpent and unit normal vectors to the space )curve (circulur helix) determined by…

A:

Q: 4. If ricost cosh t+j sint sinh t, where i and j are constant orthogonal vectors prove that (a)…

A: Given r = i cost cosht + j sint sinht

Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: Find a basis for the set of vectors in R^3 in the plane 3x - 2y + z = 0. Also state the dimension.

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Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: The relations between the unit vectors are ô, = ( sin 0 cos 4)ô, + ( sin 0 sin ø)ô, + ( cos 0)8, do…

A: We need to derive expressions A. 6-31, A.6-32, and A.6-33 by considering that A. 6-28, A.6-29, and…

Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

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Q: Find a non zero unit vecor ô that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: We have to find a non-zero vector V that is orthogonal to u1=1,2,1 and u2=2,5,4 in R3.

Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: Among all unit vectors ū = in R', find the one for which the sum x + 2y+ 3z is minimal.

A: To make the sum minimal, take two vectors u and v such that, x+2y+3z=u.v where u=<x,y,z>,…

Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

A: We need to find two distinct vectors on the line belonging to the intersection of the hyperplanes

Q: 9. Find the normal unit vector n to the surface 62 + 2y²+ 2² = 225 at the point P: (5,5, 5).

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Q: Find two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

Q: 9. Find both vectors of length 5 that are perpendicular to plane 2x + 2y +z - 4 = 0.

A: Explained below

Q: -) Are these pairs of vectors orthonormal or only orthogonal or only linearly independer [:]; » [] 1…

A:

Q: Find the divergence and curl of the vector A = rz sin ø ↑ + 3rz² cos o and evaluate both answers at…

A: Consider the given vector. A=rzsinϕr^+3rz2cosϕϕ^ The divergence formula is defined as. divF=Px+Qy…

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 =…