7. The three planes x + y + z = 0, x + 2y + 2z = 1, and 2x – y + mz = n intersect in a line. Dotor ine the values ad m for which this is tKuS

Q: show.. that the line in.which. the planes.X+zy-223D5 and. 5X-zy.-7=D0.jntersect.is. pavalle.to. the…

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Q: Which of the followings are false? I. L1 : x = 1+t, Y = -2+ 3t, z = 4 – t and L2 : a = 2s, y = 3 +…

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Q: 5) s how that the line af intersection f the Planes X+24-22= 5 and 5x-2y-73D0 is Parallel to theline…

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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: In rhombus R S T V RSTV, R S = 4 x − 2 RS=4x−2 and S T = 3 x + 3 ST=3x+3. Find the length of T V ‾…

A: The given dimensions of rhombus  RS=4x−2 ST=3x+3

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

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

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: Find the line of intersection of the planes 3x+2y-z=7 and x-4y+2z=0.

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Q: S show. that the line in..which. the planes.X+.2y-2Z=5 and. 5X-zy..Z=0..jntersect..s..pavallel.o.…

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Q: For planes 2x + y – z = 2 and 2x + 3y + 5z = 4,

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Q: 24. Consider the lines l: x = Xo +tv and m: x = x1 + su. Show that l and m intersect if and only if…

A: We will prove the given statement.

Q: 12. The line of intersection of the planes x + 2y + 3z = 1 and x – y + z = 1 |

A: Given: The line of intersection of the plane x+2y+3y=1 and x-y+z=1

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: Consider the line L(t) = (-5 – 3t, –1 – 4t,4+5t). Then: L is ? to the plane 7y – 21x – 7z = 63 L is…

A: Given the line  L(t) = -5-3t, -1-4t, 4+5t ⇒ L(t) = -5, -1, 4 + -3t, -4t, 5t ⇒ L(t) = -5, -1, 4 + t…

Q: Show that there are no points (x, y, z) satisfying 2x - 3y + z - 6 = 0 and lying on the line v = (8,…

A: Given line v is: v=8,-8,-4+t(1,1,1)  =(8+t,-8+t,-4+t) Therefore, if (x,y,z) lies on the line v, then…

Q: Find the plane through P = (4, −1, 9) containing the line r(t) =〈1, 4, −3〉+ t〈2, 1, 1〉.

A: The plane contains the line r(t)=1, 4, -3+ t2, 1, 1, so a vector in the plane is 2, 1, 1. The line…

Q: Which of the followings are false? I. L, : x = 1 +t, y= -2+ 3t, z = 4 – t and L2 : x = 2s, y = 3+ 8,…

A: We need to check whether lines interests or not

Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

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Q: 8. Determine the line of intersection between the following two planes. 8x-4y+z=12 O x+y-5z =-6 O

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Q: 24. Which of the following lines is not parallel to the other three? a. 7=(3,-5,-3) + s(2,-3,1), s e…

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Q: 3. Explain what is wrong with the following statement: If R,T are corresponding regions in the xy…

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Q: 3) Let r1(t) = and r2(t) = be two skew lines. Find the equation of the plane which lies exactly…

A: Given r1(t)→=t,t+2,2t and r2(t)→=t+1,2t+1,t+1 are two skew lines. We have to find the equation of…

Q: 11. Determine whether the lines L₁ given by x=t, y = 1+ 2t, z = 2 + 3t, (with x < t < oo) and L₂…

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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: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: Find the stundand matices * and a for ToT,OT and て:→ド,1)- (-3y, fn + 3) T:→ド, 1.(4)): (J,)

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Q: 2. Which of the following points lie on the plane 11x-2y-4z + 2 = 0 A) (4, 2, 6) B) (11,2,-4) C) (4,…

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Q: 3) Let r1(t) = and_r2(t) = be two skew lines. Find the equation of the plane which lies exactly…

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

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

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Q: 4) Find line of intersection for 2 planes.  2x-3y+z=5 -x+2y+3z=2

A: We will solve the problem

Q: Which of the followings are true? I. L1 : x = 1+t, y = -2+ 3t, z = 4 – t and L2 : x = 2s, y = 3 +s,…

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Q: 6. Determine the line of intersection of the planes X+2y +7z= 4 X+3y+3z = 1

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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: 5) s how that the line af intersection f the Planes and 5x-2y-Z=0 is Paraliel toG Pheline X+23-22= 5…

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Q: 1) which of the following pairs of planes cross along a straight line a) x+2y-3z-4=0…

A: General Equation of Plane: The general equation of the plane is given by where are constants Line:…

Q: Given: WH – Z bisector W H Y MZOWH=mZ by reason

A: Topic = Triangle

Q: 8. Check if the two lines given below are coplanar or not: x = 1+t, y =1+2t, z = 3 +t and a = 3 + s,…

A: We have to check weather the given lines are coplaner are not.

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: 1-) Determine the values of a ond b which the planes 2x -y+ 32-1=0, x+2y-2+b = 0, X+ay-6 2 +10 = 0…

A: Here, we have three planes: Plane I: 2x-y+3z-1=0; Plane II: x+2y-z+b=0; Plane III: x+ay-6z+10=0.…

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

A: topic = planes

Q: Find the line of intersection of the planes x + 7y + z = 9 and x − 5y + 4z = 15

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Q: 8. Which line does not lie on the planer = = (1,5,0) + s(2,-3,1)+1(1,-1,4), s,t € R?…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: and V is the dosed by the Planes x=0, y=O, ニこ

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Q: 6. Determine the line of intersection of the planes. X+2y +7z= 4 X+3y+3z =1

A: We use vector product to directional vector in which line of intersection of planes lies

Q: 8. Check if the two lines given below are coplanar or not: x = 1+t,y =1+ 2t, z = 3+t and x = 3+ s, y…

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Q: If p is the distance between the skew lines 4,:x=1+t, y=1+6t, z=2t Lz.x =1+2f, y=5+15f, z=-2+6t,…

A: Shortest distance between two skew lines