Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in the form ax + by + cz = d.

Q: Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection…

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Q: Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U =…

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 15у — 12z — 2 %3D 0 (a)…

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Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – = =11 and 4x + 2y – 3= =…

A: Topic:- vector

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

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Q: What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean…

A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the intersection of this plane with the line…

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Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

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Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: Find the angles between the planes in Exercises 47 and 48. 47. x + y = 1, 2x + y - 2z = 2 48. 5x + y…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

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Q: Find an equation of the plane through (-3, 8, – 7) that is perpendicular to the planes 6x – y +z = 4…

A: We need to find equation of plane.

Q: Let T be the plane x – y – z = 7. Which of the following planes are orthogonal to T and pass through…

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Q: Find the distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

A: Solution   Given,       Find the distance from  γ to the plane  in R3       spanned  by the  set…

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = Q =…

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Q: Which of the following describes a plane perpendicular to the vector n = (2, 1, -4) and contains the…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (1,1,-1) ()…

A: since plane is passing through the point (1,1,-1) and orthogonal to the vector 200

Q: Find an equation of the plane that passes through the point P(4, 6, 3) and has the vector n = (1,6,…

A: I have stated the used formula in the solution.

Q: Prove that two vectors v = (a, b) and w = (c, d)are perpendicularif and only if ac + bd = 0

A: We prove the above statement using the concept of dot product or scalar product of two vectors. The…

Q: Show that the rank of the linear mapping 7.32. Bar Y3= 301 +302 y = 201 +20203, 31-02-203 1 V2 is…

A: To prove that the rank of the matrix (representing the given linear transformation ) is 2 and to…

Q: Show that except in degenerate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: We will prove that  (u*v)*w=(u.w)v-(v.w)u u*v=ijkuxuyuzvxvyvz…

Q: Show that the vectors u=, v= , and w= satisfy the following properties of the cross product. и хи30…

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Q: Find an equation of the plane through (– 1, 3, –4) that is perpendicular to the planes 8x – y + z =…

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Q: Find an equation of the plane through (-7, 2, –6) that is perpendicular to the planes 4x – y + z = 4…

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Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Find x such that the vectors xi+2j -3k, i+j ,j+3k are Coplanars (lies the Same Plane) . on

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Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: Given points P = (2,1,5), Q = (-1,3,4), R = (3,0,6), af Find the unit vector orthogonat…

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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: Select all lines that are parallel to the plane x+y+z%= 3. OF(t) = (1,1, 1) + t(1, 1, –2) OF(t) =…

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

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Q: Let P be the plane through (1, 2, 3), (4, 3, 3), and (4, 4, 1). Find the vector of length 2 that is…

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Q: tor that is norma to the Plane determined by the three Points i+ 2j +k, si-j+ k , 3i + 2; - 7k.

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

Q: Let the vector ū = (k,5,–1) and v = (2k,k,3) are perpendicular in R', find the value of at related…

A: Given: u→=k,5,-1v→=2k,k,3

Q: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

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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: Find the point of intersection of the lines x t, y = -t + 2, z = t + 1, and x 2s + 2, y s + 3, z 5s…

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Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector

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.