Which of these planes pass through the origin? Зх — 5у+ 2z 30 5х — 3 %3D 0 = 4х + у %3D 0 — 4х — 5у + z %3 2 8х + 7у 3D 2z О бх — 5у %3D 1 6x

Q: Find an equation for the plane which contains the point P(2,1,- 3) and intersection line of the…

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Q: Find symmetric equations for the line through (1, 3, -2) and perpendicular to both u and v, where u…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Which of the following four planes are parallel? Are any of them identical?  Plane 1: 3x + 6y - 3z…

A: Given, the 4 planes we have to choose which of the four planes are parallel or identical.

Q: The diagram approximately Illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 3x+3y+3z+1=0…

A: Given planes are,    x + y + z + 1 = 0  2x + 2y + 2z + 1 = 0  3x + 3y + 3z + 1 = 0    Thus, normals…

Q: 7. Find the point or line of intersection for each system of planes a) n, = 3x – 3y – 2z – 14 = 0 П2…

A: Cramer's rule

Q: Determine the equation of the plane passing through the points P(–2, 1, 5) and Q(4, 9,-3) and…

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Q: Find symmetric equations for the line of intersection of the planes. z %3D 4x — у — 13, Z %3D 6х +…

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Q: Determine any planes that are parallel or identical. (Select all that app O P,: -90x + 60y + 30z =…

A: Find your answer below

Q: A linear combination of of u = 3 and v= 4 will give a plane in R³. Given that the point (2, 1, −1)…

A: Consider the given linear combination, u=132 and v=-144 will give a plane in ℝ3. The equation of a…

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: The scalar equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is: 2x + 5y…

A: Put the points one by one on the given planes and check satisfied or not

Q: Find symmetric equations for the line of intersection of the planes. 2 3x - y - 7, 2- Sx + 2y - 8 O…

A: Given:- Planes 1 z= 3x-y-z-7 Plane 2 z=5x+2y-8 To find:- Find symmetric equations for the line of…

Q: 6. Find the equation of the plane that passes through (3,1,2) and (-1,2,–1) and is parallel to the…

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Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

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Q: Find the equation of the set of points located three units away from the plane -2х + бу + 3z + 1…

A: Given equation of the plane, -2x+6y+3z+1=0

Q: Find an equation for the plane passing through the points Q(-2, –1, 1), R(-4, 2, 1), S(-5, –1, 2).…

A: We have been given 3 points : Q(-2,-1,1) R(-4,2,1) and S(-5,-1,2). We have to find the equation of…

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: Find the line of intersection of the given planes. 4x + y-z = 0 and 2x - y + 3z 4 %3D

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Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y-2z=3 is: O0 -3i+6j-3k…

A: Two planes are given: 4x-y+z=2 and 2x+y-2z=3

Q: Suppose the solution set of a certain system of equations can be described as x1 = 5 – 4t, x2 = -6 –…

A: Given solution set is x_1=5-4t, x_2=-6-2t ,x_3=4t-5 ,x_4=3t-3 . Now we will use the vector notation…

Q: Determine the distance between the given planes. π1 : −2x + 2y − 6z + 5 = 0 π2 : x − y + 3z + 8 =…

A: Given: Two planes are given Plane1: π1 : −2x + 2y − 6z + 5 = 0Plane2: π2 : x − y + 3z + 8 = 0…

Q: Find the equation of a plane passing through (2,1,3), (3, –1,5), and (1,2, –3).

A: Equation of plane

Q: Find a vector parallel to the line of intersection of the planes 2x + y - 3z =13 and x + 3y + 5z =-8

A: Given, The equation of the planes  2x+y-3z=13 x+3y+5z=-8 We have to find a vector parallel to the…

Q: Find the line of intersection of the given planes. 4x + y + z = 0 and 2x -y + 3z = 2

A: Given planes are: 4x + y + z = 0 2x - y + 3z = 0 Let us consider, z = t Then we get, 4x + y = -t 2x…

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: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: Find the line of intersection of the given planes. 3x + 2y + z = ~ 1 and 2x - y + 4z = 5

A: Given: 3x+2y+z=−1                                                      ...(i)2x−y+4z=5…

Q: Find the point on the plane 2x + y + 4z = 5 that is closest to the point P(4, 3, 5). (x, y, z) =…

A: We are given a plane 2x + y +4z = 5, and we are asked to find the co-ordinates of the point on the…

Q: Determine the equation of the plane passing through the points P(-2, 1,5) and Q(4,9. -3) and R(3,…

A: The given points are: P-2,1,5Q4,9,-3R3,-1,0

Q: Find an equation of the plane through (-2, 8, – 5) that is perpendicular to the planes 2x – y + z =…

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Q: Determine whether the planes are parallel, perpendicular, or neither. (a) Рi : 9х — бу + 3z 3D 4 Р2…

A: Here we will use the condition of parallelism and perpendicularity of two planes to check if the…

Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1=0 3x+3y+3z+1=0…

A: True

Q: Find the point at which the line intersects the given plane: 5x = y/2 = z + 2 and 10x - 7y + 3z +…

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Q: Find symmetric equations for the line of intersection of the planes. 4x — 2у — 2z %3 0, 2x + y + z =…

A: NOTE: Refresh your page if you can't see any equations. . system Ax=b is

Q: There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped…

A: Consider the equation

Q: Find the value of k for which the planes: 2x-ky+4z=1 and kx+y-3z%3D2 are orthogonal.

A: we have to find the value of k for which the planes 2x-ky+4z=1 and kx+y-3z=2 are orthogonal.

Q: Determine a direction vector of the line of intersection of the two planes 3x + 2y + 5z = 4 and 4x -…

A: The planes are given as- 3x+2y+5z=4........14x-3y+z=-1.........2 Solving both equations for x-…

Q: Region A is formed by bounding the lines y= T, y = 6, and the y-axis. Determine which pair %3D of…

A: Region A is formed by bounding the lines y=x, y=6 and y-axis. We have to determine which pair of…

Q: Find the point on the plane 2x + 2y + 5z = 2 that is closest to the point P(- 3, 5, – 5). (x, y, z)…

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Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: We have two planes in R3R3, defined by equations x−3y+z=−7x−3y+z=−7 and 2x+y+2z=02x+y+2z=0 . These…

A: Equation of two planes is…

Q: Find the equation of the plane through P(2, – 1,1) that is parallel to Il: 2x + 3y + z – 12 = 0. %3D

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Q: Find the equation of a plane passes through (1, 2, 3), (3,2,1) and (-1, -2, 2) ○ 4x - 3y + 4z = 10…

A: This question is based on finding equation of plane that passes through 3 points.

Q: Find an equation for the plane which contains the point P(2,1,-3) and intersection line of the…

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Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: The distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is D =…

A: topic = planes

Q: Plot the following and their normal vectors. 2x-2y + 2z = 15 3x - 3y + 3z = -13 Describe the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 7) Determine the solution of two planes 1: 2x+y+6z=4 and T2: 2x-y+2z =0, then show your answer is on…

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Q: Determine whether the planes are parallel or identical. −7x + 5y − 9z = 4 21x − 15y + 27z = 11

A: To determine whether the planes are parallel or identical :

Q: Which of the following are symmetric equations for the line of intersection of the planes 2x+y+−6z=2…

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