A unit cube (whose length, width, and height are 1 unit each) with a vertex at the origin lies in the first quadrant as shown in the figure. Express the vectors 0Q (diagonal of the cube) and OR (joining O to the center of a face in terms of î, j, and R. R

Q: Find two unit vectors in 2-space that make an angle of 45° with 7i + 4j. NOTE: Enter the exact…

A: Given :Make an angle of 45° with 7i + 4j

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

Q: Use the vectors shown to sketch u - 3v. (Assume that each point lies on the grid lines and that each…

A: Sketch the vector:  First draw the vector 3v: For -3v, the vector will change its direction.

Q: Among all unit vectors u = in R°, find the one for which the sum x + 6y + 9z is minimal. నా

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Q: Find the dot product of the following vectors →uu→ and →vv→.. Refer to image below →uu→ ⋅⋅…

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Q: 18) a) Find a unit vector that is orthogonal to both u = and v = . b) find the area of the…

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Q: Determine the two unit vectors that are orthogonal to A= . Which two unit vectors are parallel to A?

A: Given that, A = <1, 2> Suppose that <a, b> is orthogonal to the vector A = <1, 2>…

Q: Find the Euclidean inner product of the given vectors. 3 4 u = v = (u, v) = Ex: 5

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Q: Among all unit vectors u = in R°, find the one for which the sum x + 3y + 8z is minimal.

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Q: Compute the indicated vectors and also show how the results can be obtained geometrically. b-c

A: Given: b=23, c=-23

Q: 10. In the figure here, D is the midpoint of side AB of triangle ABC, and E is one-third of the way…

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Q: #1. The area of the parallelogram spanned by the vectors v = (A) – 22 (B) 22 (C) 23 (D) 8 (E) 2 (5,…

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Q: Find the resultant using (a) the parallelogram method, and (b) by summing up components. For the…

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Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

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Q: Find the dot product of the following vectors u and 7.

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Q: Determine the value(s) of k such that the area of the parallelogram formed by the vectors a = (k +…

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Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

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Q: a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides…

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

Q: Determine the real number ? such that vectors a = 3i + 2j and b = 6i + ?j are orthogonal.

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Q: Consider the regular octagon centered at the origin as shown at right. Eight unit vectors are drawn…

A: By definition, the cross product of two vectors is a vector in the direction perpendicular to the…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 31 + 2j - 3k, b =…

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

Q: (a) Find the area of the triangle with adjacent sides representing the vectors 2i – j + 3k, and i+…

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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: In Cª, find a unit vector ū that is a positive real number multiple of z = (1 – i, i, 2, 3+ 4i).

A: Introduction: For a given complex vector z=z1,z2,...,zn, its length is formulated as…

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: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k ;

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k ;

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Q: In an Euclidean space E, the vectors u+v and u - v are orthogonal, and the vectors u and u+3v have…

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Q: Find the volume of a parallelepiped spanned by vectors from the origin to the three points (1, 1,…

A: For any given three points A,B and C, area of parallelepiped is given by [A . (B X C)].

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

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Q: Find the area of the triangle with two sides given by the vectors a = i – j+ 4k, and b = 2i – 4j+1k

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Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the…

A: The given vectors a→ and b→ are unit vectors such that a→.b→=12.Given: a→+b→ and 2a→+jb→ are…

Q: In Figure , A, B, C, D,E , and F are the vertices of a regular hexagon centered at the origin.…

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Q: Find a so that the vectors v = i- aj and w = - 9i - 8j are orthogonal. (Type an integer or a…

A: As we know that; If two vectors v & w are orthogonal to each other then the dot product or…

Q: How long is the vector v = (1, 1, ..., 1) in 9 dimensions? Find a unit vector u in the same…

A: Given: The vector v= (1, 1, 1, 1, 1, 1, 1, 1, 1).

Q: Find the angle between the vectors. 20 u= - 5 531-Si and v= zi-[2 V3= 2i:

A: The given vectors are

Q: (B): Find the unit vector perpendicular to the vectors: 4i + 5j - 6k 3i - 4j+5k ;

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Q: Find a so that the vectors v=i- aj and w = 7i- 10j are orthogonal. (Type an integer or a simplified…

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Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

Q: In Figure , A, B, C, D,E , and F are the vertices of a regular hexagon centered at the origin.…

A: a=OA→  &  b=OB→

Q: (i) Which of the quantities below is equal to the area of the 2 dimensional parallelogram determined…

A: Given,

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k (PUBIEN

A:

Q: Find the signed volume of the slanted box in R" generated by the vectors 27 11 3 vi = 6. V3 = ,V4 =…

A: Given that, v1=0263,v2=-2-1-10,v3=-1-203,v4=-13-20

Q: Let each of the vectors A = 5a, -- a, + 3n,, B = – 2a, + 2a, + 4a,, and C - 3a, – 4a, extend outward…

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Q: When decomposing the vector into the sum of two vectors, the first is parallel to the vector A = 2i…

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Q: Resolve the vector a = -i+ 4j+9k into orthogonal vectors, one of which is parallel to b =i- 3j – k.

A: Given vectors are a→=−i^+4j^+9k^ and b→=i^−3j^−k^. Here, we using the concept of projection . We can…

Q: Determine a unit vector perpendicular to the both vectors A - 5i + 6j – 8k and B : - 2i + 5k. |0| =…

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Q: One of the components of cross ultiplication of the vectors A = 21 + 3 *:j + 4k and B = i-2j+3k is…

A: Given vectors are A=2i+3j+4k and B=i-2j+3k. Cross multiplication of given vectors is:…

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.