A line has parametric eauation s: x = 8 – 21, y = -9 + 3t, z = 6 – t At what time does the line intersect the plane x – 2y + 4z = 6 ? - %3D

Q: ax + by + cz + d, = 0 13) Show that the distance between the parallel planes: and ax + by + cz + dz…

A: here we have to prove the formula of distance between 2 parallel planes.

Q: Find the real number a such that the line of x = 1, y = 2-1, z=3+t, the plane of equation parametric…

A: Given parametric equations are x=t , y=2-t, z=3+t Where t∈ℝ and  Plane is αx+5y+z-10=0

Q: Find the distance from the point (- 5, 20, – 7) to the given plane or axis. If required, round your…

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

Q: let 4:x = --t, y=+t, z =+t L2:x = 2 +t, y = 3 +t, z = 1+t M: 3x + y- 2z = 3 straight lines in space…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the angle between the two planes 6x − 3y + z = 5,  −x + y + 5z = 5 and find a set of parametric…

A: We have given the equation of planes; 6x − 3y + z = 5 −x + y + 5z = 5 Hence the normal vectors of…

Q: Find the distance between the point and the plane.

A: The distance of a point from a plane in the standard equation form is equal to . The given point…

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

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: Find the distance from the point (−3,0,2) to the plane - 3x + y + 5z = 0

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Q: Ir te line x34+2¢, もー4t paralled he plane 3x +y+そこ子-

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Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0<=…

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Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

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Q: I Find the Parametric equ. sor he line f intersect of Pae Plan 3X- 6y -22 =15 and 2x+Y 2Z%=5? X-3…

A: 3x-6y-2z=152x+y-2z=5a→=3, -6, -2b→=2,  1, -2a→×b→=ijk3-6-221-2a→×b→=(12+2) i^-(-6+4) j^+(3+12)…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: find the distance from the point to the plane. (0, -1, 0), 2x + y + 2z = 4

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Find the distance from the point (-4, 5, 1) to the plane – kr – ly – 2 = 5.

A:

Q: Where does the parametric line (2 + 2t, t, t)intersect the plane x + y – 3z = 4? A) (4, 1, 1) B)1 C)…

A: The parametric line is given as (2+2t,t,t). and equation of line is x+y-3z=4 From the parametric…

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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Q: The lineL: x = 3 + 2t, y = 2t, z = tintersects the plane x + 3y - z = -4 in a point P. Find the…

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Q: Find the point where the given line intersects the given plane x = 1-t, y = t, z = 1+t, z = 1- 2x +y

A: Given lines, x=1-t , y=t  , z=1+t  Given plane, z=1-2x+y To find the point where the given line…

Q: Determine parainetric cquations for the line L representing the interscction of the planes x – y +…

A: Given equation of plane are:-           x - y + 2z = 0 and             3x + y - z = 1

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

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Q: . Let S be the part of the plane 2x - 2y + z = 1 the equation z² = 4(1 - y)²(1 - y²). Evaluation CC

A: Given that S be the part of the plane                   2x-2y+z=1 insides the "cylinder" whose walls…

Q: # 3 Let act) (cost, sint a is plane Siht) %3D Decide whether not ? curve

A: Given that  α(t)==(cost,sint,sint) Now take α(t)=(x(t),y(t),z(t)) Then, x(t)=cost, y(y)=sint,…

Q: Find the point of intersection and acute angle between Line and Plane x +1 = 4t, y -3 = t, z-1 = 0,…

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Q: ) fnd the equ. f Plane that Contains the two line S: X-1=3+ 6=そ X-リ=Z-4 and Passes through origin?…

A: Given problem:- find the equation of Plane that contains the two lines x - 1 = y + 6 = z ,    x= y =…

Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

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Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

A: I am attaching image so that you understand each and every step.

Q: Find the equation oftangent plane and normal lines of the surface: ƒ(x, y, z) = 10x² –14 y² +11z³-7…

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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: (s) (a) Find a parametric equation for the line through (2, 4, 6) that is perpendic- ular to the…

A: Equation of line in 3D

Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? A) (2 +…

A: The direction ratio of the normal vector to the plane is (3, 2,1 ) So the perpendicular line to the…

Q: Q1): Find the point (x, y, z) that lines on the plane x +y + 2z = 4 that is nearest to the origin.

A: This question can be solved using the concept of distance of point from a plane in three dimensional…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: This question is related to plane and lines, we will solve it using given information.

Q: The bearing of x from y is 045 and the bearing of z from y is 145 ,where x, y and z are three point…

A: Rules for solving Bearing and Distances: The reading in bearing is taken from North as per the…

Q: The surface given by z = x² – y? is cut by the plane given by y the point (1, 3, –8). 3x, producing…

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Q: Find the distance between the point and the plane. (0, 0, 0) 2x + 6y + z = 12

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Q: The plane through P0(2, 4, 5) perpendicular to the linex = 5 + t, y = 1 + 3t, z = 4t

A: Given: p2,4,5, x=5+t, y=1+3t, z=4t we know that equation of plane which passes through pointx1,y1,z1…

Q: Q1): Find the point (x, y, z) that lines on the plane x + y + 2z = 4 that is near origin.

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Q: Find a parametrization of the line through the origin whose projection on the xy-plane is a line of…

A: To find the parametrization of line

Q: Let P(x, y, z) be the point at which the line with parametric equatic x = 2 - t, y = 3+2t, z 1-t, te…

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Q: Find a parametrization for the line segment beginning at P1 and ending at P2. P 1(7, 2, 4) and P…

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Q: Find parametric equations for the line formed by the intersection of planes x+y-z=3 and 3x-y+3z=5.

A: First we find a point on the intersection of these planes with the plane z=0. And next find the…

Q: Find the point at which the line meets the plane. x = - 3 + 5t, y = 3+ 6t, z = - 2 + 3t; x + y +z =…

A: Given ; Line meets plane = ?   x = -3 + 5t   y = 3 + 6t   z = -2 + 3t   Plane;        x + y + z =…

Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

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Q: The surface given by z = x² – y? is cut by the plane given by y = 3x, producing a curve in the…

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Q: Find parametric equations of the normal line to *+ y? at the point (2, 2, 5) the surface z = O = 2+…

A: A detailed solution is given below.

Q: Consider the planes 2x − 3y + z = 6 and −2x + 4y − 3z = 4 Find parametric equations x(t), y(t), z(t)…

A: Given :-  The given planes are : 2x -3y + z = 6-2x + 4y -3z = 4 To Determine :-  The Parametric…

Q: (i) Find the distance from the point P(-1, 2, 1) to the plane II1 : 2x + y – 3z= 4. (ii) Find an…

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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.