Find three numbers a1, a2, az to normalize the orthogonal set 1 -2 a1 , a2 , аз 1 in R3. , az = = Ip

Q: express the vector (4,5,5) as a linear combinations of vector (1,2,3) (-1,1,4) and (3,3,2)

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

A: Topic - vector

Q: Find two vectors v, and 02 whose sum is (-5, 5, –3), where 0 is parallel to (-1, –2, 1) while Dz is…

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Q: Compute the orthogonal projection of 7 = projz (7) = onto the line L through and the origin.

A: The given data is: v→=-69 To compute the orthogonal projection of v→=-69 onto the line L through -76…

Q: Write v as a linear combination of u, u2, uz, where (a) v = (4, –9, 2), u = (1,2, –1), uz = (1,4,2),…

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Q: Write the vector (2, –3) as a linear combination of (2, –1), (–1,2) Select one: O 2/5(2, –1) +…

A: We need to find the linear combination of the given vector. NOTE - all the options given are wrong.…

Q: Determine whether the set of vectors is orthogonal. 4 2 - 4 -4 - 3

A: To determine Whether these sets of vectors are orthogonal or not.

Q: Find b and c so that  (9, b, c)  is orthogonal to both  (1, 2, 7)  and  (1, −2, 1).

A: To find b and c so that (9, b, c) is orthogonal to both (1, 2, 7) and (1, −2, 1).

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: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

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Q: The two vectors a = (-1,2,-2) and b = (2, -4,-5), are not parallel but are orthogonal. Select one:…

A: Using algebraic operation

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

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

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Q: find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A: P=-12, 92, 1,  Q=4, 6, 0

Q: as the sum of two orthogonal orthogonal to ư

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Q: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

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Q: If vectorAB =-7i + 3j + 8k and A is the point (-2, -3, 6), find B.

A: Given : AB =-7i + 3j + 8k and A=(-2, -3, 6)

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

A: Solve the given problem.

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

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

A: Here we have to plot the given vector.

Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: A vector orthogonal to the plane through the poii (-1,0,0), (0, –2, –2), (2, 3, 4) is < -2, – 10, 9…

A: The given 3 points are A (-1,0,0) , B (0,-2,-2) &amp; C (2,3,4) Let, x1=-1, y1=0, z1=0 x2=0, y2=-2 ,…

Q: The angle between the two vectors 1= (-9, –4, 7) and v = (36, 16, -28) is Select one: True False

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Q: Find a vector that has the same direction as (-4, 6, 4) but has length 6.

A: we have to find a vector that the same direction as &lt;-4, 6, 4&gt; but has length 6

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

Q: Determine if the vectors (2, –2, 1) and (0,1, 2) are orthogonal.

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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: 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: Suppose the vector ū =<3,1,-47 is translated so that it's heach is at the point C-1,2,3). where ito…

A: Given that the vector u→ = 3,1,-4 is translated such that its head is at the point (-1,2,3). We have…

Q: Determine which sets of vectors are orthogonal.

A: Given,

Q: Prove that llu + vll2 + llu - vll2 = 2llull2 + 2llvll2 for all vectors u and v in Rn

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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: Find the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)

A: Given equation is x2+cy2=1........1. We have to find the particular number of orthogonal…

Q: Define whether these vectors are linearly independent! --- u =| 2 3, 12.

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Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

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Q: Find three numbers a1, a2, az to normalize the orthogonal set 1 in R³. aj = a2 = az =

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Q: Are the vectors u=(1,2,-4), v=(-5,3,-7) and w =(-1,4,2) are in the ?same plane

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Q: Find two vectors V1 and V2 whose sum is ⟨2,−5,3⟩, where V1 is parallel to ⟨4,4,0⟩ while V2 is…

A: Parallel vector will be multiple of each other  Perpendicular vector has dot products zero

Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: Determine the orthogonality of ψ111 and ψ121 for a three-dimensional particle in a box.

A: Needed formula: ∫sin2axdx=x2-14asin2ax+Ccos A+B-cosA-B=2 sin A sin Bsin nπ=0, n=1,2,...

Q: Find a vector a that has the same direction as (-10,7, 10) bưut has length 4.

A: In the given problem we have to find a vector a that has the same direction as -10, 7, 10 but has…

Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

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Q: The vectors (-1, 2, – 1) and (2, –4, 2) are parallel and not orthogonal. True False

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Q: Find the magnitude of the projection of (- 5, 6) onto the vector (– 1, 0)

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