The vector w is a unit vector, and the vector i is any non-zero vector. If z = (x · W)w and ỹ = i – prove that vector ŷ · w = 0. %3D

Q: (2) Given u = [2 1 2]T, find a vector v so that the angle between u and v is 60° and the orthogonal…

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Q: If a = i+ 3j +k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k dw (C): If w = tan x…

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Q: 27. Find a unit vector that is orthogonal to both i +j and i+ k.

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Q: Find the unit vector e, if i = ( – 2, 2) ey =

A: Given: v→=-2, 2 To find the unit vector ev→ The formula to calculate unit vector is ev→=v→v→

Q: Find ||7e – 4f|l, assuming that e and f are unit vectors such that ||e + f|| =

A: Suppose e and f be the unit vectors such that e+f=32 First, find the dot product of the vector e…

Q: If a = i+ 2j +k and b = i+10j + k, find a unit vector with positive first coordinate orthogonal to…

A: The vectors are given as , a→=i^+2j^+k^ and b→=i^+10j^+k^ find a unit vector with positive first…

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: Let h ( x , y ) = ln ⁡ ( ( x + y ) 2 ) . If you are at the point ( e , e ) what unit vector makes D…

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Q: Find ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

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: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: Which of the following vectors are equal to j × i? i × j

A: The standard unit vectors in three dimensions, i^, j^, and k^ are length one vectors that point…

Q: et u (x, y) E R² any vector, prove that l|u||

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Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

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

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Q: Given a vector with initial point at P1 and terminal point at P2 given below, find an equivalent…

A: (2,-1) and (3,2)

Q: Consider the vector v = 1 and the vector "function" w(k) = 1 For what value of k are i and w(k)…

A: Two vectors v→ and w→ are said to be orthogonal if v→·w→=0 Given v→=111w→=11k

Q: Let b be a vector in R" satisfying the following equation. 4 3 =Db 7. Then m- and b

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Q: Find the component form of the vector v and (b) sketch the vector with its initial point at the…

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Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: The angle u= between the two vectors \(\) and U= is equal to 0=T

A: We know that angle between two vectors is given by θ=cos-1u→·v→uv Here, u→=-4,2,1 and v→=-20, 10, 5.

Q: In Fr let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

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Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: (A)Consider the given information.Let the ball is defined by the sphere and the equation with radius…

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 ||u|| for the given exercise, and give a unit vector in the direction of u.

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Q: For what value of t if any, is the vector 5t, 1] parallel to the vector (4, -1) ?

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Q: In Cª, find a unit vector ū that is a positive real number multiple of z = (1 – i, i, 2, 3+ 4i).

A: Introduction: For a given complex vector z=z1,z2,...,zn, its length is formulated as…

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: If a = i+ 2j + k and b = i+ 5j +k, find a unit vector with positive first coordinate orthogonal to…

A: Given that     a = i+2j+k and b = i+5j+k We have to find a unit vector with positive first…

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: The vectors w = x= y = and z = are linearly independent. O linearly dependent. If the vectors are…

A: The solution is follows:

Q: H.W 3- Find a vector V =xi +yj +k that is orthogonal to both A = 3i + j +k _and B = 3i +2j +2k .

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Q: Consider the vectors y= 3i + 4j + 5k and w= i + j + k. Express the given vector in terms of i, j and…

A: The given vectors v=3i+4j+5k and w=i+j+k

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: If the vector ? has constant magnitude, then show that the vector? and vector dA/dt are…

A: To show that the vector A and the vector dA/dt are perpendicular.Consider A.A = A2cos(0) = K(a…

Q: Consider the vectors cO 1 (2 1 2) (1 1 0) in R3. Find the value of c, for which given vectors are…

A: The given vectors,c01, 212, 110

Q: Find a unit vector e, where v = (4,2, 5) ey = %3D

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Q: Find a unit vector orthogonal to both u and v.u = 3i + j v = j + k

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Q: Find the velocity and acceleration vectors in terms of u, and ue. do a0 r= 9 e and :3 dt v=Ju, +Jue…

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Q: For any vectorV and unit vector U parallel to V , then D-

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Q: Q2) Suppose a vector y is orthogonal to vectors u and v. Prove or give a counter example that y is…

A: Given that y is orthogonal to vectors u and v. To show: y is orthogonal to vectors u + v or not.

Q: If a = i+ 3j + k and b = i+9j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: Given that u =, and z = What is the x component of the resultant vector w = Зи + 22

A: Given: u=4,-5z=-11,-10

Q: Evaluate /1+ x² + y²dS, where S is the helicoid with vector equation т(и, 0) - = 0 < u < 3, 0 < v <…

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 4 cos 2t and e = 5t

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Q: If a = i+ 4j + k and b = i + 8j + k, find a unit vector with positive first coordinate orthogonal to…

A: Given : a=i+4j+k and b=i+8j+k.