Suppose that i and v are vectors in R". If ū · ū = 4 and ||v|| = 9, then || 18

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: 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: Let u and v be two non-zero vectors in R". Which of the following options can we conclude are equal…

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

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Q: Prove the property if a and b are vectors and m is a real number.0 . a = 0

A: Given: If a and b are vectors and m is a real number. To prove: 0·a = 0

Q: Suppose U and W are vectors in R" then ||U +W|| - ||U|| + || W|| if the angle between U&W is equal…

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Q: Which of the following vectors is perpendicular to v = (1, –1, 3) ? о (2, —1, —1) O (-1, –1, 2) о…

A: Two vectors (a, b, c) and (x, y, z) are said to be perpendicular when their dot product ax+by+cz=0

Q: determine the x values for which the vectors of x i + 3j +4 k and 3 i +2j + 2 k are perpendicula

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Q: n Let ú and ú be two nonzero vectors in R" for which ú + 2v is orthogonal to ủ – 20. What is the…

A: We have to find the ratio

Q: \(\) The vectors u= and V = are not orthogonal if and only if x=-136

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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: 1. Prove that if u and v are vectors in Rn, then |u·v| s ||u|||v|| where ju v| denotes the absolute…

A: As per guidelines we have to attempt only 1st question

Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: \(\) The vectors u= and U= are not orthogonal if and only if x=-136 Select one: O True O False

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Q: A vector u for which || u || = 1 is called a(n)_______ vector.

A: u is a vector whose modulus is 1. u=1 For a vector, if the modulus or magnitude is 1 then the vector…

Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: The vectors į+j and i-į are perpendicular. True False

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Q: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

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Q: The vectors u and v are ________ if and only if u ∙ v = 0.

A: If the dot product of two vectors is zero ,                    If and only if they are orthogonal;…

Q: The vectors and are parallel. True False

A: Recall: ⇒ Two vectors are parallel if one is a scalar multiple of the other.         i.e, Let a→ and…

Q: If the vector u = 2i-3j+v3k , then the length of u is -v2 True O False

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: If u and v are vector in IR?, then u x v =v x u Select one: O True O False

A: False Vector product does not follow commutative law

Q: Let u, v be two vectors in IR® satisfying ||u|| = V5 and ||v|| = v2 and u. v = -2. %3D %3D Then (u –…

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

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Q: Give an example of vectors in R^3 that spans R^3. (show works)

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Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

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Q: Suppose u, v, and w are vectors in R³ and W = span{u,v,w}. Let x be a vector in R³ that is…

A: We are given that x is orthogonal to each of the vectors u, v, and w. Thus, x is orthogonal to any…

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: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

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Q: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

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Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

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: 2. Suppose that u, v and w are vectors in 3-space such that ||u|| = 5, u·v = 7, and u · w = -3 а.…

A: Answer

Q: For two nonzero vectors u and v. if u · v = 0. then u and v are orthogonal. O True O False

A: Definition: We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the…

Q: Under what condition for the real numbers a,b the vectors (b,-1)(2,a) are linearly related

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

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Q: 5b- За Let W be the set of all vectors of the form Find vectors i and v in R such that W = span {i,…

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Q: 1. Let u and v be vectors in R". Suppose ||u||2 = 2, ||v||² = 1, and u·v = 1. Compute

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Q: 8. If the vectors in the figure satisfy |u| = |v|= 1 and u + v + w = 0, what is w ? u W V

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Q: Suppose that u and v are vectors in 3-space such that |u||= 5 and u · v = 7.

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

A: Condition of dot product.

Q: Among all unit vectors ū = in R', find the one for which the sum x + 2y+ 3z is minimal.

A: To make the sum minimal, take two vectors u and v such that, x+2y+3z=u.v where u=<x,y,z>,…

Q: ind the norm of x and the unit vector u in the direction of a if -5 * = ||| = %3D 2 2

A: The norm of a vector A→=abc is defined by A→=a2+b2+c2.

Q: 64. Show that if u + v and u – v are orthogonal, then the vectors u and v must have the same length.…

A: here, the given vectors, A =u+vB=u-v given that, they are orthogonal, that is, A·B=0u+v·u-v=0⋯⋯1

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: 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: Show that for any two vectors u and v: = |

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Q: s such that vectors –si – 2j+5sk and 9si +j+3sk are orthogonal.

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Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero