What does (a b c)=0 imply with respect to the vectors: a,b,c

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

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Q: find the angles between the vectors:x+y=1,2x+y-2z=2

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Q: 'he sum and difference of two vectors à and B are equal in magnitude. Prove lgebraically that the…

A: Given: A→+B→=A→-B→ The magnitude of sum of A →and B→ is , A→+B→=A2+B2+2ABcosθ The magnitude of…

Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

Q: What geometric relationship must two vectors have in order for ||u + v|| = ||u|| + ||v|| ?

A: The expression ∥u+v∥denotes the norm of u+v, ∥u∥denotes the norm of u and ∥v∥denotes the norm of v.…

Q: C A

A: We use Triangle law

Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: Find a non-zero vector perpendicular to the vectors and ú =

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Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: How do you determine if two vectors are orthogonal?

A: If we are given two different vectors , then they are orthogonal if they are  perpendicular to each…

Q: If vector a= and vector b= are vectors a and b orthogonal, parallel, or neither? Provide

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Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

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

A: Hence the two vector u and v have same length.

Q: is The unit vector in the direction of v=(4,0,–3)

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Q: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

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Q: Determine the angle, to the nearest degree, between the vectors= (4,6,-2) and y = (1,8,2)

A: Solution is done in step 2

Q: What can you say about the relative position of two nonzero vectors if their dot product is zero?

A: Dot product of two non-zero vectors is zero. We know that two vectors are perpendicular if and only…

Q: Use paper and pencil to identify the redundant vectors. 2 1 3. 4. 3. 4.

A: We have to identify redundant vectors.

Q: What is the magnitude of the vector (2, 4, –4)?

A: FORMULA

Q: how can i learnd about vector in r2 and r3?

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Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

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Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

A: Given:- vectors <-14x, 2,1> , <2, 3x2, 10> To find:- positive value of x when both…

Q: What vector has the same magnitude as the vector u = (4,-3) and points in the opposite direction?

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Q: own your onw word, meaning for two vectors to be parallel?

A: Vectors are parallel if they have the same direction Both components of one vector must be in the…

Q: What can be said about non-zero vectors ū, v and w if (ūxv)· w = 0?

A: Here use the definition of cross product and dot product of vector

Q: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

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Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Find the area of the parallelogram that has the vectors u = (3, -1, 2) and v = (5, -4, 1) as…

A: Area of the prallelogram using cross product

Q: Find the angle between the vectors u = (2, 5) amd v =

A: Given: There are two vectors: u=2,5v=4,-3 To determine: The angle between the given two vectors.…

Q: Which two vectors are perpendicular to both å and b?

A: result of vector cross product of two vector is perpendicular to both the vectors.

Q: Consider two vectors ~a and ~b such that ~a x^b = ~0. What can be said about vectors ~a and b?…

A: We have to give the reasons

Q: how is C equal to the difference of vectors A and B?

A: Dear user, Please read the question. We need to express Vector A in terms of sum of  B and C.

Q: Find the angle between vectors v = (1,2,3) and w = (2 -1, 4)

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Q: Find the area of the parallelogram that has the vectors u = (5,-1, 4) and v = (2,-3, 1) as adjacent…

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Q: Find the angle θ between the vectors.u = (3, 4), v = (5, −12), ⟨u, v⟩ = u ∙ v

A: Given vector: Formula used : By dot product equation:

Q: Find the angle θ between the vectors.u = (3, 1), v = (−2, 4)

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Q: What helps to set of vectors linearly independent?

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Q: What is the resultant of vectors a and b? (

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Q: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

A: The two points  are : P(x1, y1, z1) and Q(x2, y2, z2). As the vector is directed from point P to Q ,…

Q: Let u and v be vectors. If their dot product is zero what is the angle between u and v (in degrees)?

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Q: Find the unit vector that has the same direction as vector v that begins at (0, -3) and ends at (4,…

A: If a vector is of the form ai^+bj^   then its unit vector along the direction v is written as…

Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

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Q: Find two vectors ūj and īz whose sum is (-5, –3), where vj is parallel to (2, 5) while īz is…

A: To find - Find two vectors v1¯ and v2¯ whose sum is -5, -3, where v1¯ is parallel to 2, 5 while v2¯…

Q: Show that if x and y are two vectors, then

A: To show : If x and y are two vectors, then x-y≤x±y≤x+y Pre-requisite :  Cauchy-Schwarz inequality…

Q: Find the angle a between the vectors 3 a || -1 -2 - and 1

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