Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w. Provide example

Q: Two vectors u and v in space are if and only if u X v= 0

A: Given vectors in space are u and v The vectors cross product is u x v = |u| * |v|* sin(angle between…

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨−7, −2⟩

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Q: Prove that if ||u|| = ||v||, then u + v and u- v are orthogonal.

A: Given: Let u and v are two vectors. To prove: If ||u||=||v||, then u+v and u-v are orthogonal.…

Q: Consider the following. u = (-10, 0, 8) v = (5, -9, 0) Find u x v. Determine if u x v is orthogonal…

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Q: What is the Jacobian of a and y with respect to u and v if = u? + 2v and y = u?v? %3D O 2u - 4u²v O…

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Q: Consider the following. u = (-3, 3, 5) v = (0, 1, 6) Find u x v. Determine if u x v is orthogonal to…

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Q: Consider the following. u = (2, -1, 0) v = (-2, 7, 0) Find u x v. Determine if u x v is orthogonal…

A: Given query is to find indicated vectors

Q: Show that u and v are parallel if and only if u×v = 0.

A: The cross product of two vectors are defined as u×v=uvsinθ. Two vectors are parallel if the angle…

Q: Prove that u and v are parallel if and only if u × v = 0.

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Q: Show that if u and v are orthogonal, then || u * v || = || u || || v ||

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Q: Consider the following. u = (-2, 5, 4) v = (0, 1, 7) %3D Find u x v. Determine if u x v is…

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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: Let w,x,y,z be vectors and suppose z=−4x−3yand w=−16x+4y−4z Mark the statements below that must be…

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Q: 3. If U and V are such that u; ='x; – A, v; =y, - B, then Cov (U, V) is :

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Q: Determine whether u and v are orthogonal, parallel, or niether. u=(-4/3,5/2) v=(16,-30)

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Q: Find the distance between

A: We use the distance formula to find the distance between u and v.

Q: Consider the following. (4,-1, 0) 7, 0) Find u x V. Determine if uxV Is orthogonal to both u and v…

A: We have given  u=⟨4,-1,0⟩v=⟨-4,7,0⟩ Then, u×v=ijk4-10-470=i0-0-j0-0+k28-4=24k

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: If u and are orthogonal to each other, then u x O True False = 0.

A: Given :u→ and v→ are orthogonal

Q: (4) Prove that if A is orthogonal, then A" is orthogonal.

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Q: Suppose that ữ, ī, and w are vectors in R3 such that uxu= (2, 7, 3) Find: %3D 1. ūxũ 2. i xữ 3. ūx…

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Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

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Q: Consider the following. u = (-6, 0, 10) v = (7, -9, 0) Find u x v. Determine if u x v is orthogonal…

A: The given vectors are  u = (-6, 0, 10) v = (-7, 9, 0)

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: 1. Let a = (1, 1, –1) and b = (2,4, 6). Find the cross product a x b and verify that it orthogonal…

A: Given: a=1, 1, -1b=2, 4, 6 To Find:  To find the cross product a×b, and, to verify that it is…

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨1, −3⟩

A: Given: v=au+bw; u=1,2,v=1,-3,w=1,-1 for finding value of a and b, we put value of u,v,w in given…

Q: Suppose we have a set of vectors v_1...v_n such that v_1 could be written as a linear combination of…

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Q: Let u, , w e R. If i and o are orthogonal and and w are orthogonal, is it necessarily true that u…

A: We will check whether the given condition is true or not.

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: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

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Q: Show that u and v are orthogonal if and only if ||u+v|| 2 = ||u|| 2 + ||v|| 2

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Q: Let w = (4,3, –1) and ở = (2,0, a). For which value of a is w orthogonal to u? Prove that there are…

A: vectors are orthogonal if their dot product is zero

Q: snip

A: Given Orthogonally diagonalize A=abba,If b not equal to zero

Q: Let u = (1,2,3) and v = (2a,2a,a2) Which of the following values of a ensures that u and v are…

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Q: if| A - B | = | A + B | . prove that A is orthogonal on B

A: Given, A-B=A+B

Q: Consider the following. u = (-3, 5, 4) v= (0, 1, 7) V = Find u x v. Determine if u x v is orthogonal…

A: To check the orthogonality , check whether the dot product is zero or not.

Q: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

A: Here, u=(1,2,3,4),v=(02,t,3) & w=(1,1,0,1)

Q: Let u = (k, 2 − k, −1), v = (2k, k, 3). Find k such that u and v are orthogonal.

A: Let u = (k, 2 − k, −1), v = (2k, k, 3)

Q: The projection of v onto w is v=i+j+2k, and w=i+2j+2k 3 =(-i+j+2k) а. (i + 2j +2k) 5 -(i + 2j + 2k)…

A: Projection vector of a⇀ on the b→ is given by c→=a→·b→b→b^

Q: Find all values of c so that (2, 1, c) and (c – 1, 2, 2c) orthogonal. are

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Q: Consider the following. u = (-3, 5, 4) v= (0, 1, 7) Find u x v. Determine if u x v is orthogonal to…

A: Topic = Vector

Q: Let p = (2, t) and q = (3,5). Find t such that p and q are orthogonal. (Give your answer in two…

A: We will use the property of orthogonality

Q: Let u=2i+3j-2k and v=-1i-4j +k Find u . v, ||u|| and u . v

A: Given that u and v vector and we find its dot product (u.v) and mode of u(||u||). Here i attached…

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: ||u+ v|| = ||u – v|| if and only if u and v are orthogonal. Select one: True False

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Q: Prove that u, v, w ∈ R3     and [ u x v, v x w, w x u] = [ u, v, w]2

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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: 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…