Determine if the vectors vị = (1,2, 3), v2 = (1,-1,–3), v3 = (1, 1, 1) span R³.

Q: Find the length of the vector.v = (4, 3)

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Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: Express the vector P, P2 in the form v = v, i+ v2j + v3k if P, is the point (- 7, - 3,1) and P2 is…

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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: photo attached

A: Given point can be written in vector form as,

Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

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Q: Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

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Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

Q: Find all values of b for which the vectors are orthogonal 〈b, 3, 2〉,〈1, b, 1〉

A: Concept - If two vectors say u and v are orthogonal, then their dot product is equals to zero.That…

Q: Find a unit vector in the direction of u = (3, 4, 5).

A: Given vector, u=3, 4, 5

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

A: the given vectors are: u=-8,-6,4v=17,-18,-1 we have to find a unit vector that is orthogonal to both…

Q: Find axb, a vector orthogonal to both vectors a' and b. a = (-3, 2, 1) and =(4, -2,5)

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Q: Find two unit vectors orthogonal to both v (1,1,-1) and w-(2,-1,1).

A: Calculation:Compute the two unit vectors as follows.

Q: are the vectors u=(-4,2) and v=(-1,2) orthogonal, parallel, or neither?

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Q: Find a unit vector that is perpendicular to both ủ = (2,1, 2) and v = (2,– 2,– 1).

A: Given, u→=2,1,2 and v→=2,-2,-1 we are asked the unit vector that is perpendicular to both.

Q: Find the resultant of the vectors A and B. Ả = A = 8a, + 7ay + 2a, B = -Зах — 8ау — ба, Draw the…

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Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

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

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Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

Q: For the vectors u = (- 1,3) and v= (- 4,2), calculate proj,u and scal,,u. proj,u = ( -2,1) scalyu

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Q: Find the angle θ between the vectors.u = (1, 1, 1), v = (2, −2, 2), ⟨u, v⟩ = u1v1 + 2u2v2 + u3v3

A: u = (1, 1, 1), v = (2, −2, 2), ⟨u, v⟩ = u1v1 + 2u2v2 + u3v3 We need to find the angle θ between the…

Q: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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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 a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v - u) -…

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Q: Let å = (- 5, 5, – 3) and b = (4, – 1, 0). Find a unit vector which is orthogonal to å and b and has…

A: Given query is to find the unit vector orthogonal to a and b

Q: Use the vectors u = (6, 6) and v = (-9, 3) to find the indicated quantity. (u - v)v (u · v)v =

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Q: Use the vectors u = (4, 4), v = (-7, 2), and w = (4, –1) to find the indicated quantity. (u · v) –…

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Find the length of the vector. v - (9, 12)

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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: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

Q: Find a unit vector which is perpendicular to both đ = (1, 1, 0) and b = (-2, 3, 0) Answer:

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Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (0, 1, 3, -1) V…

A: In  the given problem we have to find the vector v with the given length and the same direction as…

Q: Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear…

A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

Q: u

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Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

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Q: Let a and b be vectors on R³. Suppose a = (-2, 3, 482+ 1) and b = ( 8 + 1, -2, 4) What must be the…

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Q: Find all vectors u that satisfy the equation (1,1,1)×u= (−5,2,3).

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: Verify that the vectors a = (2, 5, –1) and b = (3, –1, 1) perpendicular. а. are

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