What is the size of the space stretched by the vectors {(1,0,2),(2,1,4),(1,-1,1)}?

Q: Find a vector of norm 1 that is orthogonal to the three vectors ü = (2,1,-4,0), v=(-1,-1,2,2),…

A: We have to find a vector of norm 1 which is orthogonal with the vectors u, v and w. Let a, b, c, d…

Q: Determine the volume of the box whose sides are the vectors (1, -2, 1), (2, 3, -2), (-1, 3, -2)

A: use determinant method to findout the volume.

Q: 7- Determine the volume of the parallelepiped formed by the vectors u = [ 2,1,3] , v = [1,-4,2 ] and…

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Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: 2. Find the volume of the parallelepiped formed by vectors d (-1, 2, 1), 6 = (3, –2, – 1) and T =…

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Q: Find the volume of the parallelepiped with corresponding vectors 〈2,1,0〉,〈-1,2,2〉and〈0,-2,1〉

A: Let's find.

Q: Find the volume of the parallelepiped spanned by the vectors a =(-2,3, 1), b = (0, 4, 0), and c =…

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Q: Find the volume of the parallelepiped determined by the vectors u = (1,2,-3), v = (2,4,-1), and w=…

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Q: Find the area of parallelogram with the vectors u = = (2, –2,0) and v = (0,–2,0) for sides.

A: The area of  parallelogram with vectors u=(2,-2,0)  and  v=(0,-2,0)  for sides is the cross product…

Q: compute the volume of the parallelepiped defind by the vectors v1(1,3,1) v2(2,1,-1) v3(1,0,1)

A:

Q: Find the volume of the parallelepiped determined by the vectors å = (3, 4, – 1), 6 = (0, 2, 1), c =…

A: The volume of the parallelepiped  determined by the vectors a, b and c is given by a·b×c or…

Q: Find the volume of the parallelepiped determined by the vectors = (1, 2, 3), b = (3, 0, 6) and c =…

A: This question is related to vectors, we will solve it by using the formula of volume of…

Q: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: Find the volume of the parallelepiped determined by the vectors a = (3, 4, – 1), b = (0, 4, 2), с 3…

A: Given the vectors, a→=3,4,-1b→=0,4,2c→=2,5,1

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. а 3 (6, 2, -2), ь 3 (о,…

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Q: = Find the volume of the parallelepiped determined by the vectors a c = (2, 3, 1). Volume =…

A: The volume is given by scalar triple product of vectors. a→=4,2,-1, b→=0,3,2,c→=2,3,1

Q: Determine whether the vectors a = (1,2,3),b = (1,3,1),c =(2,2,2) plane? coplanar, that is, they lie…

A: Answer and explanation is given below...

Q: 7- Determine the volume of the parallelepiped formed by the vectors u = [ 2,1,3], v = [1,-4,2 ] and…

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Q: In a 4-D Euclidean plane, vectoru = (a, b, c, d). In a 3-D space, vector v = (2,7,c). What is u + v?…

A: Given :  Vector u = <a, b, c, d>  Vector v = <2, 7, c>     To find the vector u + v.

Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

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Q: The vector (3, -1, 2) is parallel to the plane 6x – 2y + 4z = 1. - %3D

A: Use formula to calculate equation of plane

Q: A parallelipiped is constructed using vectors (8.1,2.3,0), (9.5,2.0,0) and (7.3,-2.1,7.7), what is…

A: To find the volume of parallelepiped.

Q: Find projection of vector (0,1,0) into the line spanned by (0,1,0)

A: We have to find the projection of the vector (0,1,0) into the line spanned by (0,1,0).

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Note: I have solved this above proof by two vector method but is not correct point for…

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: 5. Calculate the area of the parallelogram formed by the vectors (4, 10, 9) and (3, 1, -2).

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

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

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

A:

Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Find the area of the parallelogram that has the given vectors u = ⟨2, −1, 0⟩,     v = ⟨−1, 2, 0⟩ as…

A: Given vectors as adjacent sides are u=2,-1,0, v=-1,2,0.

Q: Determine the volume of the parallelepiped formed by the vectors P = (2,4,3), Q = (1,3,2) and R=…

A:

Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

Q: Find the volume of the parallelepiped defined by the vectors: a= (3, -1, 1), b= (4,0,2) and c=…

A: Given are the vectors  a= (3, -1, 1), b= (4,0,2) and c= (-1,-2,-3) The objective is to find the…

Q: (2, -3 ,1),(2, -3 ,5) Express the space stretched by the vectors with cartesian equations.

A:

Q: Find the volume of the parallelepiped determined by the vectors a= (3, 2, - 1), b = (0, 4, 3), č =…

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Q: 1 Which vector is perpendicular to the plane -2x + 3y – 4z = 9? 1 1 2' 3 О 2, -3,4] 2 1 9 3? О 12,3,…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

Q: Find the volume of the parallelepiped determined by the vectors a (3, 4, 1), b = (0, 2, 4), = (2, 4,…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is

A: This could be solve using vector concept.

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is

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Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

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

A:

Q: Find the volume of the parallelepiped determined by vectors , and

A: Find the volume of the parallelepiped determined by vectors <3,1,4>, <2,0,2> and…

Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: 9. Use the cross product and determine the volume of the parallelepiped generated by the three…

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Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.