2. Find the distance between the given parallel planes. 2x +y+ 2z = 8 and 4x +2y + 4z +5 = 0

Q: B. Show that line is parallel to plane x-2y + z 6

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Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

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Q: Find two di¦erent planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t . Write…

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Q: Show that the lines determined byr 1(t) = <−2 − 5t, 3 + 2t, 4t >andr 2(t) = <8 + 15t, 1 −…

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Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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Q: 3. Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x -6y + 2z = 5.

A: Given equation of planes: 2x-3y+z=4 and 4x-6y+2z=5. To find: Shortest distance between the parallel…

Q: Find the distance between the parallel planes P and P2 P: 2x-y+ 3z 6 = 0 P2: 6x - 3y+9z+ 6 = 0 8 *…

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Q: Find the distance between the given parallel planes: (a) 2x - 3y + z = 4 and 4x - 6y + 2z = 3 (b)…

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Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

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Q: a) Show that the distance between the parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is |D1…

A: (a) To show that the distance between two parallel planes Ax+By+Cz=D1 and Ax+By+Cz=D2 is…

Q: Find the equation for the plane through Po(4,9,8) perpendicular to the following li x= 4+t, y = 9+…

A: Given x=4+t  , -∞<t<∞y=9+2tz=-5tx=t=x-41 , y=t=y-a2  , z=t=-z5

Q: 4. Determine whether the planes are parallel, perpendicular or neither. If neither, find the angle…

A: Two planes are neither perpendicular nor parallel.

Q: Find the distance between the given parallel planes. 2x- 2y +z = 10, 4x-4y+2z= 1 4x – 4y+2z = 1 19…

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Q: Find the distance between the parallel planes: 3x - 4y + z = 12 6x - 8y + 2z = 2

A: Given, The equation of planes  3x - 4y + z = 12 6x - 8y + 2z = 2   We have to find the distance…

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: 1. Consider the planes P and Q given as 2x- 3y +2 = 3 and 4x- 6y + 22 = 5. Are P and Q parallel?…

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Q: Find the distance between the given parallel planes. 2z = 2y – 6x, 3z = 1 – 9x + 3y

A: Find the equation by first converting both the equation as the parallel planes then find the answer.

Q: nat is

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Q: 4. Determine whether the planes are between them. 2x – 3y + 4z = 5; x+ 6y + 4z = 3 parallel,…

A: This question can be solved using the concept of angle between two planes.

Q: is the line x = 1 - 2t, y = 2 + 5t, z =-3t parallel to the plane 2x + y - z = 8? Give reasons for…

A: Given,

Q: 7x + 3y + 4z = 5, and 21x + 9y +12z = 13

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Q: Find the distance between the given parallel planes. 4x – 5y + z = 16, 8x – 10y + 2z = 3

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Q: 5. What can you change to the two planes to make them parallel? Make as few changes as possible and…

A: given planes π5: 2x-4y+2z-2=0π6: x-y+3z-2=0

Q: Show that the line x = −1 + t, y = 3 + 2t, z = −t and the plane 2x −2y−2z + 3 = 0 are parallel, and…

A: Here we have to show that the given line,  x=-1+t, y=3+2z, z=-t and plane 2x-2y-2z+3=0 are parallel…

Q: 5) Given the point Q(2, 0, 1) and a plane p: 3x + y - 4z = 24, Find the distance from Q to p.

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Q: Consider the line L(t)=⟨4t−1,2−5t,−3−4t⟩. Is L parallel, perpendicular, or neither to the plane…

A: Lt=<4t-1 , 2-5t , -3-4t >Direction ratio of Lt=< 4 , -5 , -4 >Normal vector to given…

Q: Determine whether the line L: = 3- 2t, y=4+ 2t, z = 5+ 2t. is parallel to the plane a-y+3z 7.

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Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: 3. Determine the angle between the planes: x - z+7=0 2x +y-z+8 = 0

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Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to…

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

Q: Find the distance between the given parallel planes 4x - 5y +z = 16, 8x – 10y +2z = 3 29 a. 4/21 46…

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Q: If a? + b² + c² =1, then the distance from P (x0, y0, z0) to the plane ax + by + cz = 0 is |. |.…

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Q: Find the distance between the following parallel planes: (a) 3x – 4y +z=1 and 6x – 8y + 2z =3 (b) –…

A: Solve the above questions.

Q: Find the distance between the given parallel planes 4x – 2y+z = 16, 8x – 4y+2z=2 3 a. 3 b. 5, 14 3…

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Q: a) Find the angle between the planes 2x+ 5y -6z 0 and 3x+ 6y + 8z= 0 b) Find the distance between…

A: Given: a) Planes 2x+5y-6z=0 and 3x+6y+8z=0. b) Planes 4x-y+2z-6=0 and 8x-2y+4z+6=0. To find: a)…

Q: Determine whether the planes are parallel or identical −x + 4y − z = 6, −(5/2)x + 10y − (5/2)z = 15

A: Given information: The planes are −x+4y−z=6, −52x+10y−52z=15. Calculation: The normal vectors that…

Q: Find the distance between the given parallel planes. 2x - 4y + z = 8, 4x - 8y + 2z = 3

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Q: х —7 у-5 z-1 L: 4 -,P: 2x + y – 7z +1 = 0 6. 3

A: Given Data: Line: x-74=y-53=z-16 Plane: 2x+y-7z+1=0 Let t is a constant variable for line,…

Q: Show that the plances x + y – z = 1 perpendicular. and 2x – 3y + 4z = 5 are neither parallel nor

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Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

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Q: Find the measure of the angle between the planes 3x-4y+z=8 & 5x + y-2z = 6

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Q: Show that the line in which the planes x + 2y – 2z = 5 and 5x – 2y - z = 0 %3D intersect is parallel…

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Q: 4. Determine whether the planes are parallel, perpendicular or neither. If neither, find the angle…

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Q: Find the point at which the line intersects the given plane. x = 4 - t, y = 5 + t, z = 3t; x - y +…

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Q: Given that A and B are parallel to the yz plane, that |A| = 2, |B| = 4, and A • B = 0, what can you…

A: Consider the provided question, Given A and B are parallel to the yz plane.

Q: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Q parallel? Find…

A: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Qparallel? Find…

Q: Find the distance between the parallel planes P and P P: 2z -y+ 3z -6 =0 P: 4z - 2y + 6z - 2 =0

A: Distance between the parallel planes ax+by+cz+d1=0 and ax+by+cz+d2=0 is…

Q: x + 4y + 2z = 4, and 4x -3y +4z = 7.

A: Topic - plane and vectors

Q: x + 13y + 7z = 4, and 2x + 26y + 7z = 8

A: