[o 2B Determine the value of a, ß,7 when a -7 is orthogonal. a -ß 7

Q: Which ONE of the following formulas involving vectors a, b.c, a # 0 is meaningless? A. B. Oc. (a…

A: We have to find which formulas involving vectors  a→,b→,c→ and vector a→ does not equal to zero…

Q: Consider the following vectors: 17 -2 -2 u = | 2|, v w = and b 3 2 When b is expressed as a linear…

A: Here we solve the system of linear equation .

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: Q2 (a) Let n E N and let 7, w e R". Show that if ở - = 0, then || † + w||? = || T||? + ||||?. (b)…

A: To answer the given question we shall use the following rule: 1.   If x→∈ℝn, then…

Q: Determine the value of k so that ū = [- 5, k, 3] and i [1,2, – 7] are orthogonal. %3D

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Q: For what values of a and ß will the vector (a, 1, B) be orthogonal to (2, 0, 7) and (-1, 1, 2)? α =…

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Q: Find the best approximation to z by vectors of the form c,v, + C2V2. 3 1 - 6 2 - 1 V2 = - 3 3 1 The…

A: Solution

Q: Consider the following vectors: -3 -4 3 u = -3 , and b -2 4 4 When b is expressed as a linear…

A: Compare both side in matrix

Q: ow that c=3i -2j1+k and d=2j+ 4k are orthogonal.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

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Q: Determine whether v and w are orthogonal given v=-5i+2j and w=2i-4j

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Q: Suppose a,b and c are vectors then a.(bxc)= -(a.(cxb)) 0 صواب İhi O

A: We know that if a , b and c are vectors then

Q: 2 x=| 2 as the linear combination of the vectors u 1 Write your answer in the form x=av+bv+cw for…

A: Topic:- vector algebra

Q: Let a = (- 5, – 3, - 4) and b = (0, 1, k). Find k so that ā and b will be orthogonal. k =

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = -9i + 80j - k v = 9i + j - k O…

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Q: а - 2b a,b eR Q Assume that S= a . Is the vector (0, 4, 2) in S? Select one: True False

A: Solution is given below:

Q: Three vectors are given: A =il+j2+23,B= &4-§2+23, and C= -x4. Calculate: (a) A+B+C. (b) A+B-2C. (c)…

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Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: For what values of c are the vectors [-8, c, 4] and [c, c²,c] orthogonal?

A: For orthogonal,dot product of vectors is equal to zero.

Q: 4. Given vectors: ū=(4, 9), v = (-8, 15) and w=(2, 10) b) Write ū as a linear combination of and w.

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Q: --0--0-0) = -4 -2 R³. Determine whether the given vectors span R³. = 5 25 = -8 10

A: Given that the vectors v1=-500, v2=0-4-2, v3=25-810. The objective is to determine whether the given…

Q: Q2: Find the angle between the two vectors A = 5i - j+ 2k and B = -3i + 2j + k

A: Angle between the vector u and v is θ=cos-1u.vu.v.

Q: let V be the Euclidean space R3 with the standard inner product.

A: Given:          u = 11-2  and  v = a-12 To find :             The values of a, for which u and v…

Q: vectors are also lincarly independent: Wi = a14 + +a, W2 = d1 + + aa am +. +a

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Q: Q6:- A/ Show that the vectors A. (BxC) B.(CxÃ)=C.(AxB), if the vectors A= 31-j+2k B=21+j-k C= i-…

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Q: Consider the following. u- (9, -2), v- (4, 1) (a) Calculate projy u. projy u = (b) Resolve u into u1…

A: Given data: The points are , u=<9, -2>v=<4, 1>

Q: In R, you are given the vectors -10 u = 4 and v = -7 -39 If w = -9 belongs to Span(u, v), then what…

A: Consider the provided question, vectors,u=-34-4  and  v=-10-7-4and if w=-39-9z  belongs to Span…

Q: U= 2i-35 j V = 59 +3

A: Given: u=2i−3jv=5i+3j

Q: Find the best approximation to z by vectors of the form c, v, + C2V2 4 -7 1 1 V2 = 2 z= 3 [-1] 4 1…

A: To find  The best approximation to Z by the vectors of the form c1v1+c2v2.

Q: Q1: The following vectors; Ā =, B = 1- Find the cross product 2- Find the angle between à and B. 3-…

A: Consider the vector, A→=1,4,-1,        B→=2,-4,6 To calculate the cross product of vector,…

Q: 1. Assume the lengths of the vectors 2a – b anda+ 3b , assuming a = (2,1,3) and b = (-1,2,2)

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Let --) - -() u = |3 and v = 2 5 where y E R. Then the value of y such that u and v are orthogonal…

A: Given that, u=23y and v=-125y∈ℝThe value of y such that u and v are orthogonal is calculated as…

Q: 4. Find the value(s) of a for which and are orthogonal: a) (2,-4,5) and (a +1,3,-a +3) b) -…

A: As per guidelines we must answer only one of multiple questions given. Please resubmit the remaining…

Q: Consider the following vectors: -4 3 -4 -2 1 |, w = -2 , and b = -2 v 1 4 When b is expressed as a…

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Q: 5 Given that p andr , find in column vector form: 4 p-r ep-2

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Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: Check if each of the following is orthogonal or not: 1 [1 V2 Lo 1 i-A=D 기 ii – A = ii - A =6 v2 V2

A: We know that a square matrix of order n×n is said to be orthogonal if AAT=I  where I is the identity…

Q: Let vi = 2 v2 , V3 = -3 3 Does the set of vectors {v, ,v2, v3} span R3 ? Give reason(s) for your…

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Q: Q3: The following vectors; A =, B = 1- Find the cross product 2- Find the angle between Ā and B. 3-…

A: A→=-2, 4, 2, B→=-6, 4,- 2 1) To find: A→×B→…

Q: Determine whether u and v are orthogonal, parallel, or neither. u = -5i + 24j – k v = 5i + j - k O…

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Q: Find the indicated vector. Let u- O O [314] 82 22 77 Previous Find -2u + 5v.

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Q: Given V = {(x, y)|x > 0} where (21,1) e (22, 2) = (21*2, 1 + y2) and c o (z, y) = (r", cy), which…

A: We will use associative property of multiplication and addition both.

Q: Consider the following vectors á = 2ī+3j and b = -2ī+ 3k and c = −3ī + k

A: topic- projection of one vector on another

Q: Let V3 1 A = V2 1 1 V3 1 1 1 V2 V3 If A is orthogonal, what must x equal? Answer:

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Q: Consider the following vectors: 2 -2 and b -3 u , V 4 When b is expressed as a linear combination…

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Q: -6 --5 Let z = and y . Find the vectors v = 47, ủ =i + ÿ, and w = 47 + y. w = || ||

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Q: Find the best approximation to z by vectors of the form c,v1 + C2V2. 2 1 - 5 1 - 1 3 - 3 2 1 1 The…

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Q: If u, v, and w are vectors in Rn n>=2, and c is a scalar, explain why the following expressions…

A: Concept:   A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Consider the following. u = (2, -1,0) v = (-6, 5, 0) Find u x v. Determine if u x v is orthogonal to…

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Q: Q3: Find the angle between two vectors in space A = 41 - 2J-k B = 4T - 2J + 4k and

A: We need to find the angle between vectors A=4i¯-2j¯-k¯  and B=4i¯-2j¯+4k¯ for this we will use the…