Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of k?

Q: Given the following vectors u'and v, find a vector w in R3 so that {u, v, w} spans R3 and a non-zero…

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Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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Q: For what values of b are the given vectors o , (smallest value)

A: Let m→=-12, b,3 and n→=b, b2,b  If m→ and n→ are orthogonal.

Q: Given the vectors U =i- 2j +k, V = 2i +j+k and W = 3i - j+2k, compute the following: (a) Ux V (b)…

A: We will apply dot product formula and cross product formula.

Q: B- For what values of a1 are the vectors [a1,4,3] and [3,-2,12] are 1) Orthogonal? 2) Parallel? 3)…

A: Angle between two vector

Q: 3 Give the position vectors of A, B, C, D and E relative to O for the diagram below. B D-

A: In geometry a position vector so known as location vector. Here we find position vector relative to…

Q: If v . w = 0, then the two vectors v and w are____

A: If v . w = 0, then the two vectors v and w are____

Q: Given three vectors, u, v, and w, if u (v x w) = 0, what geometrical result can be concluded?

A: We have to conclude the result of u→.(v→×w)=0→.

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: given the vectors u = (2,4) y = (- 1,3) and w = (2, -3) Determine the values ​​of α and β such that…

A: Given vectors are  U = (2,4) so we can write it as=  2i + 4j ( i is the unit vector in x direction…

Q: If v*w=0, then the two vectors v and w are................ .

A: The question is taken from the vector in which we have to prove the given vector identity and given…

Q: Suppose that |u| = 10 and |v| = 7, and that u • v = -55. Find the angle θ between the vectors u and…

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Q: Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find:

A: (a) The angle between the two vectors u and v is computed by the following formula. cosθ=u·v|u||v|…

Q: Find the Euclidean distance between the given vectors. -- - - -8 -26 d(m, n) = Ex: 1

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: If the angle between the vectors A = xâ, +â̟and B = /3â, +â, is 60°, find x.

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Q: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

A: Given vectors a-b and a+b are orthogonal. The objective is to prove if vectors a-b and a+b are…

Q: . Given two vectors = w a = a2 show that

A: Given w→ = w1w2w3a→ = a1a2a3 We know that the cross product of w→ and a→ is w→×a→ = ijkw1w2w3a1a2a3=…

Q: Suppose that u and v are unit vectors in R°. If the angle between u and v is T/4, then what is the…

A: Given that vectors u and v are unit vectors and angle between vectors u and v is π4.  We know that…

Q: The value of k is 5 so that the vectors u= (30, 6) and v = (5, -k) are orthogonal. O True O False

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Q: 7. Find the values of m that will make the following vectors perpendicular. à = (2m, 3,1), b = (m,…

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Q: In the accompanying figure, it looks as if v1 + v2 and v1 - v2 are orthogonal. Is this mere…

A: Given figure shown below.

Q: What is the angle e between the vectors u= and v= in R* ? (Express the answer to the nearest…

A: B

Q: Suppose u = (0, –2) and v = (2, 2) are two vectors that form the sides of a parallelogram. Then the…

A: This question is based on parallelogram diagonal.

Q: Given the vectors u = (2,1,1,1) and v = (3,2, −1,2), find the value(s) of t such that I.  v . (u +…

A: Given vectors are u=2,1,1,1 and v=3,2,-1,2. To find value of t such that v.u+tv=16. Solution:…

Q: The inner(dot) product of two vectors and with lengths a and b. is given by a-b = abcos(y+2 T) ,…

A: The statement is true. The given statement is true because , Given a→.b→=abcosγ+2π But, cos…

Q: Given the vectors P=3i - j +k, Q =4i +Qy j-2k, and S=2i -2j +2k,determine the value of Qy for which…

A: given the three vectors P=3i-+j+k , Q=4i+Qyj-2k  and S=2i-2j+2k are coplanar vectors. we need to…

Q: given the vectors from R. 203, v2 (1 3 0), v3=( 2 4 -1) 203 belongs to span{v,, V2, v3}. Select one:…

A: We have to check the span

Q: Given the vectors v = 4i + 2j +k and w = 3i – 4j + k. Find | 2v – w |

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Q: b) Find the angle (0) between vectors between s = [1, –5, 4] and t = [3,3, 3].

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Q: 6. Given the following vectors, Draw: a) a-b b) 2c + a c) - (c-b) a X b of

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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: Find the angle between the given vectors to the nearest tenth of a degree.u = <2, -4>, v =…

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Q: Given the following vectors: ü =, i = Find u x v.

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Q: Find the value of a so that vectors U = ai + 6j and V 5= 9i + 12j are perpen dicular.

A: Our Aim is to find the value of a so that the vectors U=ai^+6j^ and V=9i^+12j^ are perpendicular.

Q: Given that u and vare coplanar vectors, whereu = 2i - j+ 6k andv = –3i + 5j + k, 15. u Xv = A -31i -…

A: The given coplanar vectors are  u = 2i - j + 6k v = - 3i + 5j + k To find u×v

Q: For two nonzero vectors u and v, if u v=0 then u and v are parallel.

A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

Q: Given the vectors a=(1,2,3) and b=(1,−1,2), what is the dot product a⋅b⋅a?

A: Solution :- let a = (x1, y1, z1) and    b = (x2, y2, z2)  be any two vectors then their dot product…

Q: given the vectors from R3 v, = (2 0 3), v2= ( -1 3 0), v3=(2 4 –1) %3D (-5 0 3) belongs to span{v,,…

A: Given vectors are v1→=2,0,3, v2→=-1,3,0, v3→=2,4,-1. To determine: u→=-5,0,3 belongs to span v1→,…

Q: Suppose that u and V are vectors of lengths 2 and 3, respectively. If the angle between u and V is…

A: Dot product of two vectors u and v is given by

Q: For what value(s) of a is the angle between the vectors ⟨4, 1+ 2a, 4⟩ and ⟨1, 4, 4 − a⟩ obtuse?

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Q: given the vectors from R, (-5 0 3) belongs to span{v,, V2, V3}. Select one: O True O False

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Q: 2. The area of the triangle whose adjacent sides are the vectors u and v is a) Ju · v| c) |u x v|…

A: It is known that, the area of the triangle whose adjacent sides are the vectors A and B is 12A×B.

Q: 2. Given the vectors à = (a₁, a₂, a3) and b=(b₁,b₂, b3) show that a × b = -b xã.

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Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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Q: Given that u and vare coplanar vectors, whereu = 2i – j+ 6k andv = –3i + 5j + k, 15. u xv = A -31i -…

A: Cross product of two vectors

Q: Given that the angle between the vectors a and b is n/3, then the angle between the vectors -a and b…

A: Angle between two vectors a and b is π3 Let us find the angle between -a & b  Represented in a…

Q: For what value of "c" are the following vectors perpendicular? 3 (2, с, 9) аnd ў 3 (Зс, —1,5) (Зс, —…

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Q: Under what conditions are the following true for vectors u and v in IR2 or IR3? (a) ||u + v|| =…

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

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Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.