11) (Section 9.5,9.6) Find a unit vector that is orthongonal to both u and u = (2,–1,3) v= (1,0, –2) LER (AC

Q: Find a vector å with representation given by the directed line segment AB, for A(0,3,1) and B(2,3, –…

A: We have to find the vector and draw it.

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (8y – 4xy) Give your answer in unit vector…

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Q: The vectors (3,-4,1) and (5,3,3) are orthogonal. True False

A: Topic - vector

Q: Let ū = (2, –4), ū = (0, –5), and w = (-5, –3). Find the vector x that satisfies %3D би — о +х — бх…

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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Q: A vector s has initial point (3, 4) and terminal point (5, -1). Write s in the form s = ai+bj. j

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Q: 8. Write the vector (5,6,0) as a linear combination of the vectors (-1,2,0), (3,1,2), (4,–1,0) and…

A: We have to write the vector (5, 6, 0) as a linear combination of the vectors (-1, 2, 0) , (3, 1, 2),…

Q: 6) (Section 9.4) Given u = then иnit vector in the a direction of и is

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Q: Sketch the given vector with initial point (1, 6). u = (-7, -4)

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Q: Find the projection of ū = (2, -3, 1) onto v = = (-3, 0, 1) %3D 3 0, А. B. (3.0. -1) В.

A: u→ =2, -3, 1v→ =-3, 0, 1v→ =(-3)2+02 +12       =9+1|v→| =10    u→  · v→ =2, -3, 1·-3, 0, 1u→  · v→ =…

Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1,…

A: We have to check

Q: 9. Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

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Q: Find a vector of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

Q: 11) (Section 9.5,9.6) Find a unit vector that is orthongonal to both u and v. u= (2,-1,3) v=(1,0,–2)…

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Q: make an example and prove it about five vectors spanning R⁴

A: Given: Five vector spanning R4  We need to form an example and prove the given statement 'Five…

Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: 2) (Section 9.4/9.5) Determine the value of 'a' that would make the vectors perpendicular u = and v…

A: For the vectors to be perpendicular  Then the dot product of two vectors is zero.

Q: 8. Consider the vectors [11, 2, 0, 1, 0, 2], [0, 1, 1, 2, 1, 2], [2, 1, 2, 1, 1, 1]); [0, 1, 1, 1,…

A: Remark: If no column (row) of a matrix can be written as linear combination of other columns (rows)…

Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: In each part, determine whether the set of vectors is orthog- onal with respect to the standard…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Sketch the given vector with initial point (4, 1). u = (-5, 3)

A: Here we have to plot the given vector.

Q: 9) (Section 9.4) Find the magnitude of vector u = -60i+11j

A: Given,   u = -60i+11jMagnitude of vector ; u=-602 + 112u = 3600+121  = 3721 =61

Q: 3. Show that the vectors v = (0, 3, 1, -1); v, = (6, 0, 5, 1); v3 = (4, -7, 1, 3) form a linearly…

A: Given vectors are: v1=(0,3,1,-1), v2=(6,0,5,1), v3=(4,-7,1,3)

Q: The plane that contains the points (-2,1,0), (1, 0, –1) and (0, –1, 1) is orthogonal to which…

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Q: Find the component form and length of the vector v that has initial point (3, −7) and terminal point…

A: Given: Initial point (3,-7) and terminal point (-2,5).

Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

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Q: Find a vector orthogonal to both and

A: Given query is to find the vector orthogonal to the given vectors.

Q: 9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4].

A: Given a=i+2j-3k b=2i-j+4k Aim : to find unit vector perpendicular to a and b

Q: The vectors (3, –4,1) and (5,3,3) are orthogonal. True False

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Q: What is the maximum of || Ar||∞ if ||r||∞ = 1? What is the maximum of ||Ar||2 if |-|2 = 1? For…

A: A=2123 (a) We know that Ax∞≤max∑ka1k,∑ka1k,…∑ka1k when x∞=1. Ax∞≤max2+1,2+3=5 The maximum of Ax∞ is…

Q: b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A: See the detailed solution below.

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (4y² – 5xy) Give your answer in unit vector…

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Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0,0, –2), (2,3, 4) is О О O 6,-10, 3>…

A: Let, Given vectors are P(-1,0,0), Q(0,0,-2) and R(2,3,4). We have to find non zero vector orthogonal…

Q: Chapter 11, Section 11.4, Question 033 Use the fact that the volume of a tetrahedron with adjacent…

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Q: Find scalars a, b, csuch that au + bv + cw = = (-6,12,4) u = (-1,0,2), v = (2,2,–2), w = (1,–2,1)

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Q: 8. Consider the vectors [11, 2, 0, 1,0, 2], [0, 1, 1, 2, 1, 2], [2, 1, 2, 1, 1, 1]; [0, 1, 1, 1, 1,…

A: We will reduce the matrix to see that any row can be made zero or all remain zero after operating.

Q: Find Vector production of b onto a  a=(-3,4) b =(6,7)

A: Given data: The first vector is a=(-3, 4). The second vector is b=(6, 7). The dot product of b and a…

Q: 2- We can write the vector x = (19,–1, -) in R³ as a linear combination of the vectors x1 =…

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Q: 1. Find all unit vectors that are parallel to the line going through the points (1, 3, – 1) and (2,…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

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Q: 9. Determine if the vectors å = [-1, 2, 1], b = [-2,4, 2], and ở = [12,8, 1] are coplanar. %3D

A: given vectors a=[-1,2,1] b=[-2,4,2] c=[12,8,1]

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: Find a vector b such that compab = 2. If a = ⟨3,0,−1⟩

A:

Q: Chapter 11, Section 11.2, Question 025c Find the component form of the vector v in 2-space that has…

A: We know that  ||v||=x2+y2=r||v||=8x2+y2=8=rso r=8   Component of vector v  can be written as…

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.