Find the intersection of the line r(t) = 3t + 2, 1, −7t and the plane 2x − 3y + z = 5.

Q: Q2: Find the equation of the plane that pass through the point P(-1,4,2) and containing the line of…

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Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: Find an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

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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 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: Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r:…

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Q: Find the equation of the plane passing through the point (-1, 4, 0) perpendicular to the line L₁: x=…

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Q: find the intersection point between the line      X=1+2t {    y=2-t       Z=3 and the x+y-z=3…

A: The intersection point will be common to both the line and the plane. Therefore, substitute 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 the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: Find the point of intersection between the line x+2/6 = y - 3 = z/3 and the plane x + 2y – 4z = 0.

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Q: Find the equation of the plane that contains the point P(3,5,-1) and the linex = 4 - ty = -1 + 2t,z…

A: The plane contains the point P(3,5,-1) and the line x=4-t, y=-1+2t, z=-3t

Q: Find an equation of the plane that contains the line l(t) =(-1,1,2)+t(3,2,4)y which is perpendicular…

A: As given by the question There are given that the equation of line: lt=-1, 1, 2+t3, 2, 4 And, The…

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

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Q: Find the equation of the plane that contains the line x=-1+3t, y=5+2t, z=2-t and is perpendicular to…

A: topic - equation of plane

Q: Find the intersection of the plane 4x – 6y – 7z = 10 and the line r(t) = (- 8, – 3, 3)t + (4, 1, 5).…

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Q: At what point does the line :LiX==€ 1=10+8€ 14. -2y t52 +16:0 10+3€ z=41+3€ intersect with the plane…

A: Question is based on 3d Geometry.

Q: Find the point at which the line x=1+t, y=3-2t, z=1-t intersects the plane 2x+3y+3z=0

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Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

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: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2 - 2t meets the plane 6x + 3y – 4z = -12

A: Given line is x = 2, y = 3 + 2t z = -2-2t and the plane 6x + 3y - 4z = -12

Q: Find the plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞<t<∞L2: x=1-4s,y=1+2s,z=2-2s;…

Q: Find the point P where the line x = 1+t, y= 2t, z= -3t intersects the plane x+ y -z = -3

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Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

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Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

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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: The line x=4+2t, y=-t, z=-1-4t is parallel to the plane 3x+2y+z=7 FO

A: Direction cosine vector of the line is: L=2,-1,-4 and normal vector to the plane is N=3,2,1.

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

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Q: Find the intersection of the line r(t) = (2, 1, 3) + t(3, -3, 1) and the plane 4x - 4y - 2z = 6.

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

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 equation of the plane that passes through the point (−1, 2, 1) and contains the line formed…

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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 point at which the line (-2, 2, 1) + t(5, –4, 3) intersects the plane -4x – 4y + z = -5.

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Q: Find the point of intersection of the line x = 2 − 3t y = 4 + 2t −∞ < t < ∞, z = 3 − 5t, and…

A: x=2-3ty=4+2tz=3-5tand the plane 2x+3y+4z+8=0

Q: Find the point in which the line through the (3,-1,2) perpendicular to the plane x +2y -5 z = 4…

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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: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: 2) Find the equation of the plane that is orthogonal to the planes 3x-2y-2z=1 and x-3y-10z = 4 and…

A: Given: The equation of two planes 3x-2y-2z=1 and x-3y-10z=4 and the equation of one line…

Q: The line L(t) = (2+1,8-31, 2t-6) intersects the plane 2y - 3x + 3z = -11 at the point

A: Given, the line             Lt=2+t, 8-3t, 2t-6                                   ...(1) Intersects…

Q: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

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Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: Find the distance from the line x = 2 + t, y = -2+ 2t, z = 4 – t and the plane 2x – 3y – 4z = 12…

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Q: Find an equation of the plane that passes through the point (1,1,2) and contains the line x=3t, y=1,…

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Q: Find an equation of a plane containing the line r=⟨0,−5,−1⟩+t⟨−2,4,−2⟩ which is parallel to the…

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Q: Find an equation of the plane that is passing through the point and is perpendicular to the line L.…

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Q: Find the equation of the plane through the point P = (5, 3, 3) and parallel to the plane 3y – 5x –…

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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

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.