Find the coordinate vector of v relative to the basis S = {v1, V2, V3 } for R3. v = (41, 39, 21); v1 = (7, 7, 7). (2, 0, 0), v2 = (6, 6, 0), v3 = (v)s=( i i i ).

Q: Determine (x, y, z) for each figure. Then find the component form of the vector from the point on…

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Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. -2u

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Q: Find the coordinate vector of w relative to the basis S = { u1, u2}for R². u 1 = (20, – 20), u 2 =…

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Q: Determine whether the vectors (4, 2, 3)T , (2, 3, 1)T , and (2,−5, 3)T are linearly dependent.

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Q: 21. Find the coordinate vector of x = with respect to the basis B = {v1, V2, V3} where vi =|1 V2 =…

A: Write x in linear combination of v1 , v2 , v3

Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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Q: P, find the change-of-coordinates matrix from the basis In B = {1 – 2t + t², 3 – 5t + 41², 2t + 3t²}…

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Q: Find the component form and magnitude of the vector v. Initial Point Terminal Point (-1, 5) (13,…

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Q: Find a unit vector u in the direction of the vector from P1(1, 0, 1) to P2(3, 2, 0).

A: Concept: Unit vector is a quantity which has a magnitude as 1and as well as direction, it is also…

Q: Let u=(-1,37 and u =< 2,-57 Find the Component form of the vector Su-V

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Q: Find the coordinate vector of P relative to the basis S = {p1.P2;P3} P1 = 1 +x+ x², p2 = x + x², p3…

A: Write p as linear combination of p1 p2 p3 Then the scalar in linear combination is form coordinate…

Q: Find the coordinate vector [x]B of x relative to the given basis B= {b1, b2} 3 3 b, , b2 - 7

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Q: Find r so that the vector from the point A(1,−1, 3) to the point B(3, 0, 5) is orthogonal to the…

A: The vector from the point A(1, -1, 3) to the point B(3, 0, 5)            Is orthogonal to the vector…

Q: Find the coordinate vector of w relative to the basis S = {uj, u2 } for R2. uj = (12, – 12), u2 =…

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Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2}:

A: Let us consider a vector V  with the basis b1,b2,......bn then any vector v∈V is written as linear…

Q: Find the coordinate vector of P relative to the basis S = {P1P2.P3} P1 = 1 +x+x*,P2 = x + x, p3 =…

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Q: Find the coordinate vector of w relative to the basis S = {u1, u2 } for R2 u1 = (9, – 9), uz = (3,…

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Q: Find the coordinate vector of p relative to the basis S : {P1, P2, P3} for P2. p = 15 – 21x + 12x²;…

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Q: Find the coordinate vector [x]g of x relative to the given basis B= {b, , b2}. 3 2 b, ,b2 2 -7 - 5

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Q: Find the coordinate vector of v relative to the basis S = {v1,v2, V3} for R3. v = (-11,–17, 7) (3,0,…

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Q: Find the coordinate vector of P relative to the basis S = {p1.P2,p3} P1 = 1 + x + x², P2 = x + x²,…

A: Given that , S=p1,p2,p3p1=1+x+x2 , p2=x+x2 , p3=x2 , p=5-x+8x2 PS=?

Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find the coordinate vector of v relative to the basis S = {v1, V2, V3 } for R3. v = (13, 4, 8); Vi =…

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Q: The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

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Q: 17 (c) Find a unit vector which is orthogonal to the vectors -1 2 and 1 -3 5

A: First we will find a vector which is orthogonal to both given vectors and then we will find the unit…

Q: Find the position vector for the vector having initial point P and terminal point Q. P = (-2, -3, 1)…

A: Find a and b by subtracting the x and y values for the terminal point minus the initial point.

Q: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: Find a unit vector that is orthogonal to both u and = (-8, -6, 4) v = (17, -18, -1)

A: In this question we will use basic of calculus i.e vector calculus. We will simply find the cross…

Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

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Q: Find the coordinate vector of w relative to the basis S = {u1, u2} for R2. : (6, – 6), u2 = (2, 2);…

A: Here we have to find the coordinate vector of w relative to the basis S ={u1,u2} for R2 . Here…

Q: Find the coordinate vector of w relative to the basis S= = (u1, u2) for R. Let u = (2, –3), u2 = (3,…

A: Given

Q: Find the coordinate vector of v relative to the basis S = {v1, v2, V3} for R3. v = (-11,–17,7) V1 =…

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Q: Find the coordinate vector of v relative to the basis S = {v,, V2, V3} for R³. (b) v = (5, –12, 3);…

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Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 3u…

A: u=-3, 4 &amp; v=2, -5 a). 3u-4v=3-3, 4-42, -5=-9, 12-8, -20=-9-8, 12--20=-17, 32

Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: Find the coordinate vector of w relative to the basis S = { u1, u2} for R u 1 = (4, – 4), u 2 = (4,…

A: Given: u1=4,-4u2=4,4w=0,24

Q: Find the coordinate vector of P relative to the basis S = {p1,p2.P3} P1 = 1 + x + x², P2 = x + x²,…

A: p1=1+x+x2, p2=x+x2, p3=x2; p=3-x+9x2

Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: Use vectors =(-1, 1), v= (7, –2), and w= (0, 4) to find (u w)v, and determine whether the result is…

A: We can answer it as below

Q: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

A: Given: Let A(7,6,2) and B(2,14,2) be the two points the line passes through To find: vector equation…

Q: Find the coordinate vector of v relative to the basis S = {V1, V2, V3 } for R3. v = (11, 3, 8); vị =…

A: Find coordinate vector of v relative to basis S

Q: 5. Find a nonzero vector orthogonal to the plane through the points P(1,0, 1), Q(-2, 1, 3), and R(4,…

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Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

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Q: . Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x +2, 2x…

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Q: Find the coordinate vector for the vector v = (3,4,3) relative to the basis S={(3,2,1), (-2,1,0),…

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Q: Find the coordinate vector of w relative to the basis S = { u1, u2} for R². u 1 = (5, – 5), u 2 =…

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Q: Find a vector orthogonal to the vectors ā = and 5=.

A: Recall:  Vector orthogonal to the vectors a→ and b→ is a→×b→a→×b→ We have, a→=1,2,3, b→=1,0,1