(A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 If the plane meet with the line x-+2t, y -2t and z 1+t?

Q: 20. Find the point at which the line a = 1+ 2t, y = 4t, z = 2 –t intersects the plane r+y – 2z +1=…

A: Given that, equation of line:- x=2t, y=4t, z=2-t Equation of Plane:- x+y-2z+1=0

Q: The equation of the plane that contains the point (1, 2, 3) and the line x = 4t, y = t, z = t is…

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Q: A. Find the angle between the planes x+y+z 1 and x-2y+3z 1, and Find symmetric equations for the…

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Q: 2. Find the distance of the point A : (1,0, 2) from the plane P: 3x +y+ z = 9.

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

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

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Q: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

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Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Determine the general equation of the plane Ω passing through the point P(1,−4,−5) and parallel to…

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Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

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Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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Q: The line X=t, y+1=t, Z=t intersects the plane. x-2y+Z=2 at the point

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Q: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

Q: A. Show that the planes (x+y- z = 1) and ( 2x - 3y + 4z = 5 ) are neither parallel nor…

A: Let's find.

Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

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Q: Consider the plane P with equation 2x-2y+z =4 and line L with equations x= 3+2t y =-1-5t z= 5+4t…

A: Solved below

Q: The plane 6x + 8y + 60z = 700 intersects th of the highest and lowest points or coordinates

A: Given that the plane           6x+8y+60z=700  and the cone                            z2=x2+y2

Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

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Q: Find the point on the plane x+ 2y - z 12 that is nearest the origin.

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Q: Find the point in which the line through the origin perpendicular to the plane 2x – y – z = 4 and…

A: We have to find the point in which the line through the origin perpendicular to the plane 2x-y-z = 4…

Q: find the distance from the point to the plane. (0, 1, 1), 4y + 3z = -12

A: we have to find the distance of the point (0,1,1) from the plane 4y+3z=-12.   as we know that the…

Q: Find the plane containing the intersecting lines x = -1+t, y = 2+ t, z =1–t; -0 <t < o∞ | L2: x = 1…

A: Find the planes containing the intersecting lines: L1:x=-1+t,y=2+t,z=1-t for all…

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

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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: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

Q: Find an equation of the plane in standard form (ax + by + cz = d) that passes through the point (4,…

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Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: A. Show that the planes (x+ y– z = 1 ) and (2x – 3y+ 4z = 5 ) are neither parallel nor…

A: let the normal vectors for the vectors be a1, a2 thus a1=&lt;1,1,-1&gt; and a2=&lt;2,-3,4&gt;. Let…

Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z=12

A: As there are multiple questions, the first one (19) is solved here.

Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

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Q: Find the point on the plane x - 2y + 3z = 12 that is closest to the point (0, 2, 2). (x, y, z) =

A: Just I have used the Lagrange multipliers method and find the required solution.…

Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

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Q: Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = =…

A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: Q3/ Find the plane determined by the interseetiny Lines L X=1-2t, , 3-st,,そニ-2+t, La.Xe-3+t2)…

A: To find equation of plane we need to first find point and direction ratio of lines. Then find…

Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 8 If the plane meet with…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: What is the distance between the point A(1,-1,3) and the plane x + 2y + 2z + 1=0 ?

A: To find The diatance between the point A(1,-1,3) and the given plane

Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

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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 a plane that is perpendicular to the two planes x + y = 3 andX + 2y - Z = 4.

A: Since we have been given two planes x+y=3-(i) and x+2y-z=4-(ii)Our Aim is to find a plane that is…

Q: Find the point on the plane 3x + 2y + z = 6 that is nearest the origin.

A:

Q: An equation of a plane P passes through the point (0, 0, 3) and perpendicular to the line L:x =1 –…

A: Remember that the vector (l, m, n) is parallel to the line with parametric equationx=a+lt, y=b+mt,…

Q: Find the points on the plane r - y = 2 – z closest to the point (1, 1, 1).

A: We will find the closest point on the given plane as following.

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: Find the distance from the point Q to the plane p. Q= (0, 0, 0), p with equation x - 2y + 2z = 1

A: GivenQ=0,0,0p:x−2y+2z=1

Q: Find the equation of the plane in the form z = c + mx + my containing the line in the xy-plane where…

A: Plane

Q: Does the line r(t) = intersect the plane 5x - 2y - z = 21 and if so, where?

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Q: Determine the Cartesian equation of a plane that is perpendicular to the plane x - 2y + z = 6 and…

A: Given : A plane x-2y+z=6 and which contains a line -x+2-3=y+1=z+12  To find: The Cartesian equation…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.