t u - (1,1, -2) аnd v = (a, –1, 2). For what values of a are u and v orthogonal?

Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

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Q: find the distance d(u, v) between u and v in the given exercise.

A: We will use the formula

Q: Please solve this linear algebra question. Thank you

A: According to the given information, It is required to show that u, v, w are linearly independent…

Q: If |r(t)| = c (a constant), then r' (t) is orthogonal to r(t) for all t.

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Q: of the motion of r(t) = . Leave your a

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Q: find the distance d(u, v) between u and v in the given exercise.

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Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

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Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: Find the length and direction (when defined) of u x v and vxu. u= - 12i + 9j – 12k, v = - 4i + 3j –…

A: Using formula of u x v and v x u,

Q: For what values of h is v3 in span {v1, v½} and for what values of h is {vi, V2, V3} linearly…

A: Given vectors  V1=133 , V2=39-1, V3=-2-6h 1) V3=Span{ v1, v2} 2) V1,V2,V3 is linearly dependent.

Q: Let v = -7i - 7j-3 k and w =-3i+ 4j +6 k. Then the vector v – w can be written as

A: note : vector addition or subraction can be performed as  a⇀+b→ = (ax+bx,ay+by,az+bz) similarly for…

Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

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Q: Find u × v and show that it is orthogonal to both u and v.u = (−2, 1, 1), v = (4, 2, 0)

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Q: Compute u x v. (a) u = 2i + 3j+ 4k, v = -i+ 3j – k (b) u =i+ k, v = 2i + 3j – k (c) u =i-j+ 2k, v =…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: d) Prove that ||vxw||²+|v-w[? = ||v||²|w||² for all vectors v, w in R3

A: Prove the following

Q: Find u × v and show that it is orthogonal to both u and v.u = (2, −3, 1), v = (1, −2, 1)

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Q: Find u × v and show that it is orthogonal to both u and v.u = j + 6k, v = 2i − k

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Q: Compute u x v. (a) u =i-j+ 2k, v = 3i +j+2k (b) u = 2i + j – 2k, v = i+3k (c) u = 2j + k, v = 3u 4…

A: To compute: u×v. If we have two vectors A=x1i+y1j+z1k and B=x2i+y2j+z2k then: A×B=ijkx1y1z1x2y2z2…

Q: Let y = #₁ = 1 and = 2 -27 -2 Write y as the sum of two orthogonal vectors, 1 in Span{u} and 2…

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Q: Which of the followings is the vector projection of u onto v where u = -2i + 4j – V5k and v = 2i –…

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Q: Find u × v and show that it is orthogonal to both u and v.u = (1, −1, 1), v = (0, 1, 1)

A: Cross product is,

Q: find the distance d(u, v) between u and v in the given exercise.

A: We need to find the distance between the two vectors.

Q: Find u × v and show that it is orthogonal to both u and v.u = i − 2j + k, v = −i + 3j − 2k

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Q: Find u × v and show that it is orthogonal to both u and v.u = (−1, 1, 2), v = (0, 1, −1)

A: Given vectors

Q: Find u × v and show that it is orthogonal to both u and v.u = (1, 1, 0), v = (0, 3, 0)

A: We have given; u = (1, 1, 0), v = (0, 3, 0)

Q: Compute the length of the given vector. (t) = 2t + 7 and q(t) = 7t - 5, where to = 0, t₁ = 1, t₂ = 2

A: We have to find the length of the given vectors.

Q: X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/…

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Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w? Explain your…

A: Given that 'x' is orthogonal to 'v' and 'w' . This implies x,v=0and x,w=0

Q: Find u × v and show that it is orthogonal to both u and v.u = (4, 1, 0), v = (3, 2, −2)

A: Now cross product is,

Q: 1 Suppose v, = -3,v2 = 9. V3 For what value(s) of h is vz in span{v,,v2}? How do you know? b. For…

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Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Let T: R3→R3 be defined by T(a, b, c) = (a+ b, b −2c, a + 2c). For each vector v in R3, determine…

A: Given: A linear transformation defined as:

Q: Find u × v and show that it is orthogonal to both u and v.u = j + 6k, v = i − 2j + k

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Q: for any R value of the third, so that the following vectors are linearly related and loudspeaker…

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Q: Find a vector function r(t) that satisfies r′′(t) = [6t, −2t−1/2, 1], r′(1) = [0,1,0],and r(1) =…

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Q: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

A: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

Q: Determine R21, the vector from P2(5,2,–4) to P1 (3,–1,0). 2аx + Зау — 4а, —2ах — Зау + 4az 4ax + ay…

A: Consider the following vectors: P→1=3ax-ayP→2=5ax+2ay-4az…

Q: 11) For u = (2,3,-1) and v (-1,01) find; %3D II a) proj,(u) b) The vector component of u orthogonal…

A: For finding projection using the formula, projv(u)=v→.u→v→2v→ The vector component of u orthogonal…

Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

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Q: Consider the vector-valued function F(2,) = [xy² + 2ye* х, у y 3xe-y Which of the following are NOT…

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Q: Let y = T-97 –3 and i = 5 7 4 -2 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2…

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Q: Let S = { t² + 1, t² – 1, t – 2}. - 2. If S is linearly independent in P2, write 2t2 – t + 5 as a…

A: Three vectors A,B,C are said to be linear dependent, then there exist three numbers a,b,c such that…

Q: Find u × v and show that it is orthogonal to both u and v.u = (12, −3, 1), v = (−2, 5, 1)

A: Given vectors u=12,-3,1v=-2,5,1 Their cross product is u×v=ijk12-31-251…

Q: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!

A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…

Q: Please see image

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Q: Let B= { }],19} be basis for IR. %3D Find [v]g where V= 15

A: Given :                          Basis  B = 3-30, 22-1, 114 and V = 15-93…