Find the equation of the plane Π that contains the lines L1: x=−1−2s, y=1−t, z=−1+4s, s∈R L2:x=5+2t, y=6−3t, z=7+8t, t∈R Write the equation of the plane in the form ax+by+cz+d=0.

Q: 5) Find the equation for the plane perpendicular to the plane P and containing the line L, where P:…

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Q: Find the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

Q: The two planes r+y +z= 1 and r – 2y + 3z = 1 intersect in a line l.

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Q: (b) Find an equation of the plane that contains the line x = 1 + t, y = 2-t, z = 4 - 3t and is…

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Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: Find the equation of the plane which passes through O and is parallel to z – (5x + 6y) = 3 x+ y + z…

A: see 2nd step.

Q: The equation of the plane passing through the point (0, 0, 4) and perpendicular to 4 is: the line 4…

A: Equation of plane

Q: find the plane containing the intersecting lines.  L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

Q: Find an equation of the plane that contains the point P(5,0,2) and the line x = 3t +1, y=-2t + 4, z…

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Q: Find the equation of a plane through the point (- 1,1, 3) and orthogonal to the line ( x(t) = – 7 –…

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Q: Find an equation of the plane containing the lines L1 and L2 in R3 L1: x = t ; y = -t ; z = t L2:…

A: We have to find equation of plane containg Line L1 and L2  -

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

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 an equation of the form ar+by+cz = d for the plane that passes through the points A(3,2,0),…

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Q: only part b

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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,…

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Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1 and…

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Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

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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 Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

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Q: Find the equation of the plane through the point (2, –1, –5) and containing the line | x = 3 – 2t, y…

A: We have to find the equation of the plane, passing through the point (2,-1,-5) and containing the…

Q: Given the planes π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Find the equation of the…

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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: Find an equation for the plane parallel to the liner =1- 21, y = 2 + 3t %3D 2 = 1+ 2t and that…

A: Given: Plane is parallel to the line x=1-2ty=2+3tz=1+2t Also, the plane contains the line of…

Q: Find an equation of the plane through the point (2,0, 1) and perpendicular to the line x = 3t, y = 2…

A: To find the equation of a plane passing through (2,0,1) and perpendicular to the line x=3t , y=2-t ,…

Q: Find the point of the intersection of the plane P: 2x - 3y + 4z + 14 = 0 and the line L:r = 1 – t,…

A: Given the equation of line and plane  2x−3y+4z+14=0x=1−ty=1+tz=2+3t

Q: Find the equation of a plane through the intersection point of the lines r(t) = and 7(s)= where r, s…

A: The equation of plane is mainly given by the normal vector calculation. The normal vector to the…

Q: Find the equation for the plane through Po(4,9,-7) perpendicular to the following line. x-4+t,…

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Q: Find the equation of a plane through the point(- 3, – 2, 3) and orthogonal to the line x(t) - 5+ 8t…

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Q: H.W: Find the point where the line 8 x=+ 2t , y= -2t , = 1+t intersects the plane 3x + 2y +6z = 6

A: Given that:                    The line with equation:      x=83+2t, y=-2t, z=1+t     & Plane:…

Q: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the lin l1…

A: Let's find.

Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

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: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

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: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: Find the cartesian equation of the plane determined by the two intersecting lines x-4 y+1 z-2 L1: 3…

A: Here,  v1=3i+2j+kv2=5i+3j+2k v1×v2=ijk321532=i4-3-j6-5+k9-10=i-j-k Thus, the equation of the plane…

Q: Find the point of intersection between the line r(t) = + t and the plane 4x + 5y + 3z = 5. o a. (…

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Q: Find the point at which the line r(t) y(t) z(t) = -6-7t 7+t - 54t intersects the z plane.

A: Let's find intersect points.

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: For the plane, 6x + 10y + 15z = 30, the values of the x-, y-, and z-intercepts are %3D 5, 3 and 2 3,…

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Q: Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 15 –t and L2 : {…

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Q: Write the equation for the plane through the point P(- 4,4,2) and perpendicular to the line x =4+7t,…

A: Explanation of the answer is as follows

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2). O…

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Q: Find the equation of the line of intersection of the following two planes: Plane A: 2r – 3y + 2z =…

A: Given Plane A : 2x - 3y + 2z = 5Plane B : x + 2y - z = 4To find the intersection point, Put z = 0 ,…

Q: . Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 2+8 L1 : 4 -t…

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Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

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Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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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.