The Cartesian components of the position vector r in a general coordinate system are given by 1 1 = uv cos 6, y = uv sin ø, z=;(u² – v²), where (u, v, ø) are known as paraboloidal coordinates. We shall choose { = u, &² = v and F³ = 6. 1.) Find the covariant and contravariant base vectors corresponding to the paraboloidal coordinates. Is the coordinate system orthonormal, orthogonal or neither?

Q: Find the vector v with the given length and the same direction as u.||v|| = 4, u = (−1, 1)

A: To find a vector v with the given magnitude of ||v|| = 4 and in the same direction as u = (−1, 1).

Q: The norm of the vector v= - i+10j-8k is ||v||=, (Round your answer correct to 3 decimal places)

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Q: 1or Find. Ewo unit Vectors in X-y plane 30 deyree with the vectur that make angle cf V= 3i +4j ?

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Q: Find a vector, AB , with magnitude 4 in the direction of PQ where P and Q have coordinate (5,0, 8)…

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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: Find cos(0) if 0 is the angle between the vectors u= 2i + 2j – k and v = 3i + 4k

A: Consider the two vectors. u=2i+2j-k and v=3i+4k It is given that θ is the angle between the vectors.…

Q: Given the point D(−4, 5, 3) and A = yax + (x + z)z ay, express the D and A in: Kindly answer in…

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Q: When analyzing the vectorĀ = 2i – j + 3k To the sum two vectors, the first is parallel to the vector…

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Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

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Q: When the angle between vectors u and v is between 0° and 90°: || You can't tell O t • 0

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Q: 3) Find the components of the vector i that has a magnitude of |0| = 9750N and direction 0 = 243.0°-…

A: Find the components of vector v. |V| = 9750 θ= 243.0o

Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

Q: Find a vector v parallel to u=4i−3k and with magnitude ||v||=4

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

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Q: Find vector u with the magnitude given that satisfies the given conditions. v (7, -1, 3), ||u || -…

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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 the magnitude only for the vector from T(-2, 6, 1) to U(10, -3, -4).

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Q: Find the vector ū which satisfies the given conditions. i =, Ju| = 2 , ū and i have opposite…

A: The unit vector,  , in the direction of the vector is calculated as follows.

Q: 1. The two unit vectors parallel to the line y = x- 3 are and

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

Q: Dados los vectores u=2i-3j+4k y v=(4,1,-2) , calcular la norma (módulo) del vector u - 2v V37

A: Given: u=2i-3j+4k v=4,1,-2

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

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

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Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

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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 unit vector which is perpendicular to both r1=8ax+3ay-2az, * r2=2ax+7ay-6az is equal to a)…

A: Given That: The unit vector is perpendicular to r1=8ax+3ay-2az & r2=2ax+7ay-6az

Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find a. cos(theta), where theta is the angle between…

A: As we know that; The expression for the dot product between the two vectors u & v is: u·v=uvcosθ…

Q: Find a unit vector that is orthogonal to both i+j and i+k ?

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

A: Follow the procedure given below.

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: what is u.v when u and v are two unit vectors with an angle of (pi/6) between them. if u=i and if v…

A: Given: u=i, angleθ between u and v=π6 let's assume v=xi+yjx2+y2 we know that angle between two given…

Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

A: Given: X(1, -2, 1) and Y(0, 3, -2).

Q: Suppose that u, v are vectors in R³, u · v = 1, || = 1, the angle between u and v is T/3, and u is…

A: According to the problem, we have

Q: 1. Given three vectors u =(1,–3,0), v=(2,1,–1) and w=(0,2,3). Determine: a. Bu + 4v – Sw]. b. Cosine…

A: 1. a.

Q: For what value(s) of a is the angle between the vectors ⟨4, 1+ 2a, 4⟩ and ⟨1, 4, 4 − a⟩ obtuse?

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Q: If the position vector of a particle P is r(r) (3cos t,5sin7,4 cos t) a) Show that the speed of the…

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Q: Find the second and the third components of a vector n normal to the plane with the equation 7x +…

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Q: A line L has a direction vector v = 2i t 4j+ v5k and passes through the Find the distance between…

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

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

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

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Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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Q: b) Find equation of the Plane through point (1, 2, 3) parallel to the vectors V1 = 2i + 3j + k and…

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Q: Given the following points, determine the vector equation defined by having point A as initial point…

A: RCS- Rectilinear Co-ordinate System CCS-Cylindrical Co-ordinate System SCS- Spherical Co-ordinate…

Q: If A = 3i + 4j and B = 7i + 24j, the %3D vector having the same magnitude as B and parallel to A is…

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Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.

Q: Find the horizontal and vertical components of the vector u that has magnitude |u|=4 and direction…

A: Given that, the magnitude is |u|=4 and the direction angle is α=20∘