b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when they are positioned so their initial points coincide. Prove that x v sin e %3D

Q: Find two unit vectors orthogonal to both u (3, – 1, – 2) and i (0, 4, 2). Give exact values - (no…

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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: 6. List 3 non-zero vectors in R° that are orthogonal. (You must verify that they are orthogonal.)

A: See the detailed solution below.

Q: 23. Show that u + v < u + v for any vectors u and v.

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Q: Find a unit vector u in the direction of v. Verify that ||u|| = 1. v = (-6, 6)

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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: find the component form of vector RS with the initial point R(3,-2) and terminal point S(3,3)

A: From the given problem:   Initial point R3,-2   Terminal point S3,3   So the component form of RS→:…

Q: Prove that u · v = 1/4 llu + vll2 -1/4llu - vll2 for all 4 4 vectors u and v in Rn.

A: Given Data The equation to prove is u∙v=1/4||u+v||²-1/4||u-v||².   Evaluate the right hand side for…

Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: find a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8),…

A: The parametric equation of a line in vector for is given by the expression r→=u→+tv→. Here u→ is the…

Q: The scalar projection of vector A onto another vector B will be the negative of that scalar…

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Q: Find a unit vector perpendicular to both u = (2,3, –4) and v = (-1,1,–4). %3D

A: The unit vector perpendicular to u and v is given by: w=±(u×v)|u×v|

Q: Find two unit vectors orthogonal to both u = (1, 2, – 3) and = (0, 1, 2). %3D unit vectors =

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Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

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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: Let u be the vector with initial point p( 5,1) and terminal point q ( 2,2,) express u in terms of i…

A: NOTE: Refresh your page if you can't see any equations. . the initial point is  and the terminal…

Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector x + y. :Select one…

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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 unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

A: The given vectors are u=(0,1,1) &amp; v=(1,0,1).

Q: 19. Find two unit vectors perpendicular to vector u= (7, 0, -1) and vector v = (1, -1, 1).

A: We have to find the unit vector

Q: Consider the vectors u = ⟨cos , sin , 0⟩ and v = ⟨cos , sin , 0⟩, where &gt; . Find the dot product…

A: Consider the given vector u→=cosA,sinA,0 and v→=cosB,sinB,0

Q: Find the vector in R° from point A = (x, y, z) to B = (-2, –4, 1).

A: Given points  A  = (x,y,z) B = ( -2,-4,1) To determine the vector in R3 from point A to point B

Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector x+ y. :Select one…

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Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

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Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=&lt;0,-2,1&gt;Hence, Vector…

Q: Find the smallest positive angle between the given pair of vectors. (3,1) , (4,6)

A: The given pair of vectors are,

Q: Describe all vectors v that are orthogonal to u

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Q: Find the angle 0 between the vectors. 5T u-(cos , sin S), v-(cos, sin 4) = 4 4 3

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Q: Find a unit vector u in the direction of v. Verify that u|| = 1. v = (-6, -4)

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Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: Find a Vector ū: non zero Vector perpendicular to the

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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: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is

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Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

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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: 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: Compute the cosine of the angle between the plane through P – (6,0,0). Q = (0, 5,0), and R = (0,0,9)…

A: (a). Given points are P6,0,0, Q0,5,0 and R0,0,9. We know that equation of plane through a,0,0, 0,b,0…

Q: Find the angle θ between the vectors.u = (0, 1, 0, 1), v = (3, 3, 3, 3)

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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 vector perpendicular to the vectors -2 and ü = 2 ||

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Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(-5,-3)

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Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

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Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0). LO î + 27 (F (smaller i-value) î…

A: Use the given information.

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

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Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

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Q: ind a vector orthogonal to both u and j+k. u=2i-j+3k

A: we have been given two vectors,  u = j+k. v=2i-j+3k   the unit vector that is orthogonal to both…

Q: Find the values of x such that the angle between the vectors ⟨2, 1, −1⟩ and ⟨1, x, 0⟩ is 45 . (Pls…

A: The angle between the vectors ⟨2, 1, −1⟩ and ⟨1, x, 0⟩ is 45 degrees. We need to find the value of x