Prove Ảx (B x Č) = B(Ả C) – Č(Ã B) is true by expanding Ả, B, and components (or Cartesian corrdinates). č vectors in â, ŷ, 2

Q: Suppose A and B are non-zero vectors in R. If A•B = 0, then A and B are parallel. True False

A: Follow next step

Q: Prove that for any non-zero vectors a, b, a · b = |a||b| cos(0), where 0 is an angel between a and…

A: Consider the n -dimensional vectors a and b , where n≥2 . The vectors a , b and a−b can be…

Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

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Q: Let v, w, and a be nonzero vectors such that v · a = w · a.Is it true that v = w? Either prove this…

A: Given: v, w and a is non zero vectors, such that: v·a=w·a To prove: v=w

Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

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Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: v=2i+4j  and  w=-3i+6j. Now, v·w=2i+4j·-3i+6j=2-3+46=-6+24=18 & w=-32+62=45=35 Therefore,…

Q: Prove that if x and y are vectors in R", then |||x|| – ||y||| < ||x- y||. X

A: Given x and y are vectors in Rn we have to prove that x−y≤x−y Since, x=x Hence,  x=x−y+yAdd and…

Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: 1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Prove that if the vectors a,b parallel, then āxb=0. are %3|

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Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

Q: Prove that for any vectors u, v, w , the set span{u+v,u – v, 3u – 3v + 2w} contains u, v, and w .…

A: A vector v is said to be contained in span of set S  (span(S)) if vector v can be written as a…

Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: Determine all vectors v that are orthogonal to u.u = (4, −1, 0)

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Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

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Q: Let x and y be two orthogonal vectors. Then prove that +

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Q: Prove that the vectors v= and w= are orthogonal.

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Q: Suppose that ā and b are nonzero vectors. Under what circumstances is comp;b = comp;a? Under what…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: Determine all vectors v that are orthogonal to u.u = (11, 2)

A: Now let

Q: Prove that two vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0

A: we have to prove that the two vectors v=a,b and w=c,d are perpendicular if and only if ac+bd=0

Q: Show that if u is a vector in R2 or R3, then u + (−1)u = 0.

A: The objective is to show that if u is a vector in R2 or R3 then u + (−1)u = 0. Suppose u and O is a…

Q: Show that if u and v are vectors in an inner productspace that satisfy the Pythagorean law||u + v||2…

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Q: Prove that a·a= = |a|2, where a is a vector with n components

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Q: . Prove that (only one): E - 4y-V3ay is a unit vector? a- F 2 b- A = 6ax - 3a, + 2a, and B = 3a, +…

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Q: Le and ü .Write j as the sum of two orthogonal vectors, a, in Span {u} and i2 orthogonal to ū.

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Q: Prove that A.B + |A x B| < 2|A||B| for arbitrary vectors A, B and C.

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Q: prove that 12 div A; = √√√x² {√8 8¹k Ax} = dxr div A¹, where A; and Ai are the covariant and…

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Q: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: For any vectors u, v in R', we havelu + ū|? = [u|2 + [ū]2 True False

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Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

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Q: Let x = (1,2,3) and y = (1,1,1) Project y on x (in econometrics, this may be denoted by Px). Are the…

A: We will first write the formula for projection of a vector onto another vector b .

Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: 3. For any vectors U, V and scalars a, b, prove that (a) (aU) x (bV) = ab(U x V)

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Q: Show that if u is a vector in R2 or R3, then u + 0 = u.

A: To show that if u is a vector in R2 or R3, then u + 0 = u.

Q: Show that if u + vand ủ – v are orthogonal, then the vectors u and must have the same length

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Q: Prove that |A|B + |B|A is orthogonal to |A|B – |B|A, for any vectors A and B.

A: We need to show that |A|B + |B|A is orthogonal to |A|B – |B|A, for any vectors A and B. Here, |A|…

Q: Q3. Prove that (only one): ax-V3ay a- is a unit vector? b- A = 6ax – 3a, + 2a, and B = 3ax + 2a,y –…

A: Given two statements . We need to prove only one out of that  So, here we will prove first statement…

Q: Find all vectors in R2 that are orthogonal to u = (2,1).

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Q: Consider the two vectors A = Axî + Ayĵ and B = Bxî + Byĵ. If î · î = ĵ • ĵ = 1 and î · j = ĵ · î =…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

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Q: If x = (x1, x2)T , y = (y1, y2)T, and z = (z1, z2)T arearbitrary vectors in R2, prove that xTy = yTx

A: x = (x1, x2)T , y = (y1, y2)T are arbitrary vectors in R2 .

Q: Show that the following vectors of v,(R) are LI : a, = (1, 1, 0); a, = (1, 1, 1); a, = (2, 1,3)

A: Introduction :

Q: If i • ( or v• (u x w) or w • (u x 7) equal to zero, then the 3, and w vectors u. are coplanar.…

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Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

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