If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The coordinates :of P is

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: 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: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

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: Show that the lines determined byr 1(t) = < 7, 3 − 4t, 2 + 6t> andr 2(t) = <6 − t, 3 + 8t,…

A: Given: r1(t)=7,3-4t,2+6t r2(t)=6-t,3+8t,9-5t For r1. x-7=y-3-4=z-26=t For r2. x-6-1=y-38=z-9-5=t…

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: Show that the planes given by y − 7z = 16 and 2y − 14z = 5 are parallel, and find the distance…

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Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

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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: 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: To find the equation of a plane which cuts intercepts a, b, c res- pectively on the axes of…

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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: @/ Find the angle between the planes (x-+y+z=1)and (x-2y+32-1). And find the symmetric equations for…

A: Given equations of planes are x+y+z=1 and x-2y+3z=1 Here, a1=1,b1=1,c1=1 & a2=1,b2=-2,c2=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: 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: Find the plane that contains the point (0, 1, 2) and the line x = 1- t,y = 2 + t,z = 4 + 3t.

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

Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: Find an equation for the plane that contains the line x = − 1 + 3t, y = 5 + 3t, z = 2 + t and is…

A: We need to determine the equation of the plane that contains the line: x=-1+3t, y=5+3t, z=2+t and is…

Q: Find the point(s) of intersection (if any) of the plane 2x + 3y = 10 and the line (x − 1)/3 = (y +…

A: The equation of line x-13=y+1-2=z-3=r(arbitarary point) then x = 3r +1 y = -2r -1 z = r+3

Q: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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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: 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: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: ) At what point does the line: L: x =- t, y = 10 + 3t, z = 4 + 3t intersect with the plane n: x – 2y…

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Q: C. Show that the lines with symmetric equations (x y z) and (x+1 are skew, and find the distance…

A: L1 ;  x=y=z     x-01 =y-01=z-01  x1=0    y1=0     z1=0α1=1    β1=1      γ1=1L2:  x+1=y2=z3…

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: the plane whose intercepts with X zagy = b,Z=C show that the Coordinate axes are has equation Ą + +…

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Q: What can you conclude if you know that the point (p, q) lies on the line y = mx + b?

A: We have to conclude if the point p, q lies on the line y=mx+b. We know that if any point is lying on…

Q: Given two lines L1 : x =t+1, y = 3t + 1, z = 2t – 1, and L2 : x = 2t – 2, y = 2t + 3, z =t +1,…

A: The given lines are L1:x=t+1,y=3t+1,z=2t-1L2:x=2t-2, y=2t+3, z=t+1 and a plane H is parallel to both…

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: Given the planes (x, y, z) = (0,0, –3) + s(1,1,–2) + t(-2, –-1,3), and x + y + z + 6 = 0 : a) Are…

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Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

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Q: find point b (x,y) given that M (7,3) is the midpoint of line A(10,4) and b

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Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

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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: If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-3z=0 are orthogonal to each other.…

A: The parametric equation of the given line is  x=1+a+2ty=1-btz=-1+c-1t The general form of the…

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: Show that the lines with symmetric equations L1 : = = and L2 : 팡!%3D 부 =D 촬 %3D y-3 are skew.

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Q: find the point in which the line meets the plane x = 1 + 2t, y = 1 + 5t, z = 3t; x + y + z = 2

A: Given, The equation of line x = 1 + 2t, y = 1 + 5t, z = 3t and the equation of plane is x + y + z =…

Q: Prove that the perpendicular distance from the point P(xo, Yo, 20) to the plane with equation ar +…

A: Here we use the distance formula between two points.

Q: Find the point at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t   -1and plane , x+2y-z=6

Q: Find Sax ds, where C is the line segment in the plane joining (0,0) and (3, 4).

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

Q: , in general form (x + y2 + Bx + Cy + D = 0), centered a he lines 2x + y + 10 = 0 and x - 2y - 5 = 0…

A: We have to find the equation of a circle whose center is the point of intersection of,  2x+y+10=0…

Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…

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

A: Topic - plane and vectors

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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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.