Find the equation of a plane through the point (- 1,1, 3) and orthogonal to the line ( x(t) = – 7 – 8t y(t) = 5 – 7t - z(t) - 2 – 6t

Q: 1. Find the equation of the plane that contains the point (-1, 1, 2) and the line given by x=1-t,…

A: This question is based on 3d geometry.

Q: Q1// A :- Find an equation of the plane that passes through point (1,4,3) and contains the line…

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Q: Find an equation of a plane containing the line r = (2, –2, 3) + t(12, –8, 4) which is parallel to…

A: Equation of plane parallel to the plane 4x+4y-4z=-17 is of the form  4x+4y-4z=k This plane contains…

Q: 20. Find the point at which the line a = 1+ 2t, y = 4t, z = 2 –t intersects the plane r+y – 2z +1=…

A: Given that, equation of line:- x=2t, y=4t, z=2-t Equation of Plane:- x+y-2z+1=0

Q: Find the point(s) of intersection of the line x = 1 – t, y = t, z =1– 2t - and the paraboloid z = 8…

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Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

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Q: Find the scalar equation for the plane passing through the point P=(-5, -2, –4) and containing the…

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Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

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Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

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Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: Example 8: Find the point where the line 2t, and z = -3t intersects the plane x = 1 + t, y = –…

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Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

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Q: 3. Find the general form of the equation of the plane containing the point Q(0, -2, 10) and the line…

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Q: Find an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…

A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…

Q: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

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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: Find the scalar equation for the plane passing through the point P=(4, -5, 3) and containing the…

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Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

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Q: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  xz

A: Let the plane P whose equation is:                                          3x-9y+4z=5…

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: 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: Determine the general equation of the plane Ω passing through the point P(1,−4,−5) and parallel to…

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Q: 15. Find an equation of the plane through the point (-2, 4, 6) and perpendicular to the line r = t,…

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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 = -3

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Q: Find the equation of a plane through the point (1, – 1, 6) and orthogonal to the line x(t) = 7 + 4t…

A: Required plane is orthogonal to the given line, say L: x(t)=7+4ty(t)=-3-4tz(t)=-1-6t also, the plane…

Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

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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: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

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Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

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

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Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

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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: Find the point on the plane 2x + 3y + z = 7 that is nearest to​ (2,0,1).

A: NOTE: Refresh your page if you can't see any equations. . the given point is . the given plane is…

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

A: r(t)=3t+2, 1, -7t and the plane 2x-3y+z=5

Q: 3. Find the equation of the plane containing both the point (1, 2, 3) and the line r(t) = (t, 2t+1,…

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

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: (b) Find the points on the line r(t) = (t, 1+2t, 1-2t) whose distance from the plane 2x - 2y+z=1 is…

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Q: Find the scalar equation for the plane passing through the point P-(0,-3, 2) and containing the line…

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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 plane determined L1: x=-1+t 12: x=1-4s by the intersecting lines: y=2+t y=1+2s 2=1-1-3-1-00…

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Q: Find the point on the plane 3x + 2y + z = 6 that is nearest the origin.

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Q: An equation of a plane P passes through the point (0, 0, 3) and perpendicular to the line L:x =1 –…

A: Remember that the vector (l, m, n) is parallel to the line with parametric equationx=a+lt, y=b+mt,…

Q: Suppose a particle P in R' is traveling upward in a straight line which is perpendicular to the…

A: Given: Suppose a particle P in R3 is traveling upward in a straight line which is perpendicular to…

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 perpendicular to each of the planes z – y+z = 0 and 2r+y-4z–5 =0 and…

A: The given problem is to find the equation of plane perpendicular to each of the given planes and…

Q: Give an equation of the plane whose trace in the yz-plane has equation y = 6z, and in the xy-plane…

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Q: Find the equation of the plane passing through the point P(1,-1,2) and parallel to the lines =Dz and…

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