Can three vectors in the xy plane, R^2, have u.v<0, v.w<0, w.u<0

Q: Write down the equations of any two distinct planes with normal vector n = 〈3, 2, 1〉that do not pass…

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Q: 436. The plane that passes through point (4, 7, -1) and has normal vector n= (3, 4, 2)

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Q: The plane with normal vector (0, – 2, – 4) containing the point (-7,4,-3) has equation Aæ + By + Cz…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find two unit vectors orthogonal to both u (3, – 1, – 2) and i (0, 4, 2). Give exact values - (no…

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Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: Find linearly independent vectors which generate al lutions of Ax = 0.

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Q: Find 3-dimensional vectors V₁, V₂, V, satisfying V₁V₁ = 4, ₁₂ = -2, V₁ V₂ = 6, V₂ V₂ = 2₁ V₂ V₂ =…

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

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…

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Q: A hiker begins at the origin and walks in a straight line in the direction of the vector (1,1) for…

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Q: cannot be found in such a general cas explain why. In either case, justify you 2) Let a and b be two…

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Q: Let(vector u)=(-2,-3), (vector v=(-3,-5) and vector w=(-2,-3). Find the vector x that satisfies…

A: u=(-2,-3)v=(-3,-5)w=(-2,-3)Calculating x:

Q: Find projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

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Q: Find an equation of the plane through the point (4, 5, 1) and with normal vector 6i + j - k. Show…

A: The plane passing through a point A(a) with the normal vector n is given by: r·n=a·n where,…

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: Find the vector n= normal to the plane passing through the points (0, -3, 0), (2, -1, 0) and (-2,…

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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: Find a vector of length 2 orthogonal to the plane 3x – 4z = 5. %3D

A: Here we have to find the vector of length =2 and  orthogonal to the plane 3x - 4z = 5 Let the vector…

Q: Verify that the two planes are parallel. -x + 6y + 3z = 7 1 --x+2y +Z 8 Find the normal vector, n,,…

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Q: Find an equation of the plane through (1, −3, 5) with normal vector n =〈2, 1, −4〉.

A: Consider the given: Point on the plane is P = (1, -3, 5) Normal vector to the plane is n→=2,1,−4 Let…

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: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

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Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

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Q: Write the equation of the plane with normal vector n = i - k passing through the point (5, 2, –8) in…

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Q: Calculate the area of the parallelogram which is bounded by two vectors given as www ā = (x, y,z),…

A: Calculate area

Q: A vector orthogonal to the plane through the poii (-1,0,0), (0, –2, –2), (2, 3, 4) is < -2, – 10, 9…

A: The given 3 points are A (-1,0,0) , B (0,-2,-2) &amp; C (2,3,4) Let, x1=-1, y1=0, z1=0 x2=0, y2=-2 ,…

Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

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

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

Q: Find two unit vectors orthogonal to both (3,2,1) and (–1,1,0).

A: The vectors 3,2,1 and -1,1,0

Q: Write the equation of the plane with normal vector n passing through point Po in the scalar form ax…

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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: Find the equation of the plane with normal vector n = (8, 7, 3) passing through the point (4,,9) in…

A: Use equation of plane and put value

Q: Find two unit vectors that are normal to the plane determined by the points A (0, -1, 3),B (2,…

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

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Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

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Q: Compute the cosine of the angle between the plane through P – (6,0,0). Q = (0, 5,0), and R = (0,0,9)…

A: (a). Given points are P6,0,0, Q0,5,0 and R0,0,9. We know that equation of plane through a,0,0, 0,b,0…

Q: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

Q: Find an equation of the plane that passes through the point P(-2, –4, 2) and has the vector (-5, 4,…

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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: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: 4. Find an equation for the plane through (1, 3, 4), with normal vector .

A: topic- equation of plane with point and normal vector

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 two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: to Dara bala y=XZ. Find the unit vectors that are parallel to the tangent line Dara bola y = x² at…

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Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…