Consider the line which passes through the point P(-3, –3, –1), and which is parallel to the line x =1+t, y = 2 + 2t, z = 3 +t Find the point of intersection of this new line with each of the coordinate planes: xy-plane: xz-plane: yz-plane:

Q: Find the points where the liner(t) = 4 − 3t, 8 + 7t, 5 + t, −∞ < t < ∞,intersects each of the…

A: The point where the line intersects co-ordinate planes, one of the co-ordinates must be zero.

Q: Find point P where the given line intersects the given. Plane or decide that the line aoes not…

A: For finding intersection point, substitute the values of x, y, z given in equation of line in…

Q: Let a and b be real numbers. Let L be the line defined as L:x = 6 – 6t, y= -11+t, z= a +bt, te R Let…

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Q: Consider the line which passes through the point P(1, -3, -2), and which is parallel to the line x =…

A: Given: The vector equation of the line is: x=1+4t;y=2+7t;z=3+1t r→=123+t471 so the line is the…

Q: Find the point at which the line intersects the given plane.

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Q: Find the point​ (if it​ exists) at which the following plane and curve intersect.   z=13​; r​(t)=t,…

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Q: Which of the following is the equation of a plane parallel to the cz-coordinate plane and passing…

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Q: Ex(29):- Determine whether the line and the plane are intersect; if so, find the point of the…

A: Given, The equation of the line   L : x=t, y = t, z =t  Equation of the Plane : PL : 3x-2y+z-5=0…

Q: Consider the line which passes through the point P(5, 5, -5), and which is parallel to the line x =…

A: Equation of the line :       x-x0a = y-y0b = z-z0c=k ; where x0,y0,z0 is a point and a,b,c is the…

Q: Determine whether the line L and plane PL are intersected, if so, coordinates of intersection point…

A: NOTE: Refresh your page if you can't see any equations. . the given line is introduce the variable…

Q: Find the point of intersection, if any, of the plane T: 4x + 2y – 2z=1 and the line l : 3 +t 1

A: Point of intersection of line and plane

Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Let L be the line x = 3t + 1, y = −5t, z = t. (a) Show that L lies in the plane 2x + y−z = 2. (b)…

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Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 – t, z = 3 + 2t. Write…

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Q: Determine the distance between: the pa rallel line x-a++ X - 3+S+t t9= 5-t,tER and the…

A: Given line is                                                     x=2+ty=5-tz=-4 point on the line…

Q: Find the point at which the line intersects the given plane. x = 2 − 2t,    y = 3t,    z = 1 + t;…

A: Given that  x = 2 − 2t,    y = 3t,    z = 1 + t;    x + 2y − z = 4 first we will substitute values…

Q: Consider the line which passes through the point P(3, -1, -1), and which is parallel to the line x =…

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Q: Let a and b be real numbers. Let L be the line defined as L :x = 5 – 5t, y = -9 + t, z = a + bt, teR…

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Q: Let a and b be real numbers. Let L be the line defined as L : x = 6 – 6t, y= -11+t, z = a + bt, teR…

A: Given that L be the line defined as                  L : x=6-6t, y=-11+t, z=a+bt, t∈ℝ   where a,b∈ℝ…

Q: Find the point of intersection of the lines given below and then find the plane determined by these…

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Q: Determine whether the plane x + y + z = 9 and the line x = t, y = -2t + 1, z = t + 2 are parallel,…

A: The given equation of line is in parametric form, x=ty=-2tz=t+2 Convert it into the cartesian form,…

Q: Let a and b be real numbers. Let L be the line defined as L :x =7 – 7t, y = -13+t, z= a + bt, teR…

A: Give line L: x=7-7t, y=-13+t, z=a+bt, Plane D: 10x+6y+z=16 ⇒L: x-7-7=y+131=z-ab…

Q: Find the point of intersection of the lines given below and then find the plane determined by these…

A: A detailed solution is given below.

Q: Let L be the line defined as L: r = 5 – 5t, y = -9 + t, z= a + bt, teR Let D be the plane defined as…

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Q: Consider the line which passes through the point P(5, 2, -1), and which is parallel to the line x =…

A: Introduction: In three dimensional geometry, there are three fundamental planes referred to as the…

Q: Find the distance from the point Q= (2,2,2) to the line of intersection of the planes x+y+z=1 and…

A: Distance from the point Q(2,2,2) to the line of intersection of planes x + y + z = 1 and x + y = 2

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

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Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

A: We will solve the problem

Q: 2. Assume that the plane P3 is perpendicular to the yz-plane, and the line l2 : x = 2t, y = t, z =…

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Q: Consider the line which passes through the point P(-2, 4, 3), and which is parallel to the line x =…

A: Consider a line  L1:x=1+7t,y=2+7t,z=3+4t Point : −2,4,3

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: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let a and b be real numbers. Let L be the line defined as L : x = 7 – 7t, y = -13 +t, z = a + bt, te…

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

A: Given:   Plane→   2x+3y = 10  Line→       x-1 3= y+1-2 = z-9

Q: Let a and b be real numbers. Let L be the line defined as L: a = 7 – 7t, y = -13 + t, z= a + bt, teR…

A: Idea: line and plane are parallel then line perpendicular to normal to the plane. By using this idea…

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

A: Given line, x-14=y2=z-36And given plane3x+4y=-7Any  point on the line isx-14=y2=z-36=tx-1=4t,y=2t,…

Q: Let a and b be real numbers. Let L be the line defined as L: x = 5 – 5t, y = -9 + t, z = a + bt, teR…

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Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7)…

A: Given: Parametric equation of line l: (x,y,z)=(3,-1,7)+r(-5,2,1) Equation of plane: 2x+3y+4z=24

Q: is cut by the plane given by y = the point (1, 3, -8). 3x, producing a curve in the plane. Find the…

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Q: Let a and b be real numbers. Let L be the line defined as L:x = 6 – 6t, y = -11 + t, z= a + bt, teR…

A: Given :- parametric eqn of a line L. And also we are given equation of the plane. We use vector…

Q: Find the distance from the point (– 4, 21, - 5) to the given plane or axis. If required, round your…

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Q: Find the point of intersection of the lines given below and then find the plane determined by these…

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Q: Let Li be the line whose equation in symmetric form is y - 2 _ 3-2 ,z 2. 3 Let Lz be a line normal…

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Q: Consider the line which passes through the point P(-5, 4, 4), and which is parallel to the line x =…

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Q: Determine an equation of the form Ax t t Cz + D=O By for the plane that contains the line (x,y,2)=…

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Q: Let a and b be real numbers. Let L be the line defined as L: x = 4 – 4t, y =-7+t, z= a + bt, t e R…

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Q: Let a and b be real numbers. Let L be the line defined as L : x = 6 – 6t, y = -11+t, z= a + bt, teR…

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

A: Given line x-38=y2=z-714=tAny point on the line is of the form,x=3+8t,y=2t,z=7+14t,Put…

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.