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

Q: Give the component form of the vector represented by the directed line segment from (4, 5, 6) to (4,…

A: See this  solution in below

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: 4. Add a vector to the set S {(1,0,0,00), (0,0,-2,0), (3,0,0,0). (0,9,0,0)} to make it span R* %3!

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Q: Compute the orthogonal projection of 7 = proj,(v) = 4 [1] onto the line L through -4 and the origin.

A: Given:    Data is given

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: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

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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: Compute the orthogonal projection of i -5 onto the line L through -4 and the origin. proj, (5) =

A: Here we use for product to find he projection.

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

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Q: Find a vector a with representation given by the directed line segment AB. A(-1, 5), B(2, 4) Draw AB…

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Q: Find the unit vector represented by the directed line segment with initial point A (-2,1,1) and…

A: The vectorAB = B-A=(2,-3,4) -  (-2,1,1) = (4,-4,3) So the unit vector is :…

Q: Find the largest linearly independent set of vectors from the list given below. V2 = vz = %3D

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Q: Determine whether the points are coplanar.(−4, 1, 0), (0, 1, 2), (4, 3, −1), (0, 0, 1)

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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: Use vectors to determine whether the points are collinear. (4, −2, 7), (−2, 0, 3), (7, −3, 9)

A: Formula: the vectors a, b and c are collinear if detabc=0.

Q: as the sum of two orthogonal orthogonal to ư

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Q: If P = 1 - 3, 12 and Q = 1x, 42, find all numbers x suchthat the vector represented by PQ >has…

A: Given :               P = (-3,1)   and Q = (x,4)                  PQ→ = Q - P      = x+3,3PQ→= x+32…

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 X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

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Q: Determine the figene valves and Vector for 2 A=-1 2 -2

A: (A-λI)X=0 A= given matrix λ=constant I=identity matrix

Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

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Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

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

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Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

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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: Show that the set as; S = {(1, 1, 1), (2, 3, 3), (0, 1, 2)} spans R^3, write the vector (4,6,7) as a…

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Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

Q: Determine whether the points are coplanar.(−3, −2, −1), (2, −1, −2), (−3, −1, −2), (3, 2, 1)

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Q: Determine whether the points are coplanar.(1, 2, 3), (−1, 0, 1), (0, −2, −5), (2, 6, 11)

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

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Q: A set of 3 vectors in IR^4 spans IR^4. Is this true or false?

A: Given statement is, “A set of three vectors in R4 spans R4.”

Q: Find a vector a with representation given by the directed 个 line segment AB, where A(–6, −6) and…

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Q: Let A, B, C be points in 3-space. Suppose that AB represents u, BC represents v, AC represents W.…

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Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: Prove that the points position vectors collinear. With at 26, 2a-5 and 3a-46 are

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

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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: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

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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: 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: 9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or…

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

A: Here, a1 , a2 and a3 are unit vectors . w1 = (1,-1,3)  w2 = (-2,1,1)  w3 = (4,7,1)

Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: Find two vectors a and b such that projba = &lt;4, -2, 8&gt;. That's all the information I was…

A: It is given that,

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

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