Determine an equation for the plane that passes through the point (1, 2, –3) and is parallel to the plane x – 3y – 2z – 4 = 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 equation of the plane in the form z=c+mx+ny containing the line in the xy-plane where x=3,…

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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 Cartesian equation of the plane containing the point P(1,3,-2) and the I T = (0, -1, 4) +…

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

A: The trace of the plane in yz plane is obtained by substituting x=0 in the given equation of the…

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 coordinates of the point where the line F = (1+ 2t)i + tj – 2tk intersects the plane 2x – y…

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

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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: Find an equation of the plane tangent to the surface 4x2 + y2 - 12z = 0 and parallel to the plane 8x…

A: In the question given it is asked to calculate the equation of plane in terms of z where the…

Q: Find an equation of the plane. The plane through the point  (6, 0, 1)  and perpendicular to the line…

A: Given, The plane through the point (6, 0, 1) and perpendicular to the line x = 7t, y = 8 − t, z = 5…

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 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 trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

Q: Find an equation of the plane. The plane that passes through the point (2, 3, 5) and contains the…

A: We need to find the equation of the plane. x=5t , y=2+t , z=3-t Plane passes through (2,3,5) the…

Q: Find an equation of the plane. The plane that passes through the point (1, 3, 5) and contains the…

A: Given linex=5t , y=1+t , z=3-tDirection vector of this linev⇀=5,1,-1coefficients of t

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 equation of the plane through the point P=(5,2,5) and parallel to the plane 2y−4x−z=9. z=

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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: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

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Q: Show that the curve a(t) = (t,4,²) lies in a plane and find the equation of this plane.

A: Solution:- αt=t,1+tt,1-t2t t,1t+1,1t-t=x,y,z It is clear that, t-1t-1+1t-t=x-y+z x-y+z=-1

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

A: Given,

Q: Find the equation of the plane: The plane that passes through the point (3, 4, 5) and contains the…

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Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, yz

A: Let the plane P whose equation is;                                      -x+y=4…

Q: Find an equation for the plane through the point (3, 4, −4) and parallel to the plane defined by 4x…

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

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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 an equation of the plane. The plane that contains the line x = 3 + 2t, y = t, z = 6 - t and is…

A: We will find the equation of planes.

Q: The line L(t) = (4 – 3t, 3, 1 +t) intersects the plane 3x – 3y + 2z = -16 at the point when t =

A: To find the point of intersection of the line and the plane, substitute the values of x,y, z from…

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 an equation of the plane. The plane through the point (4, 0, 2) and perpendicular to the line x…

A: To find- Find an equation of the plane. The plane through the point 4, 0, 2 and perpendicular to the…

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 7z + 13 =…

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Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

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Q: 3. Find the equation of the plane perpendicular to the plane x + 2y + 3z = 11 and passing through…

A: Equation of plane passing through one point (a,b,c) and normal vector n = <A,B,C>…

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: Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = =…

A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: ) Find the equation of the plane passes through the point P(2, 2, 3) and perpendicular to the two…

A: To find the equation of the plane that passes through the point P (2, 2, 3) and perpendicular to the…

Q: Find an equation for the plane that passes through the point (1, 2, 3) parallel to u = 2i + 3j + k…

A: Given:u = 2i + 3j + k and v = i - j + 2kFirst find cross product

Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 8 If the plane meet with…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: Find the equation of the plane Π that contains the lines L1: x=−1−2s, y=1−t, z=−1+4s, s∈R…

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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: Find an equation of the plane. The plane through the point (4, 0, 1) and perpendicular to the line…

A: Given that, Let, the required equation be, lx-a+my-b+nz-c....(1) The required plane passing through…

Q: Find the equation of the plane through the origin that is parallel to the plane 4.r – 2y+ 7z +12 = 0…

A: Consider the general equation of a plane, 4x-2y+7z+12=0 the normal vector of this plane will be…

Q: H.W 8- Find equations of the planes that are parallel to the plane x +2y- 2z= 1 and two units away…

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Q: Find the point on the plane x – 3 y – 2 z = 14 that is closest to the point (0, 3, 3) .

A: We have the plane x-3y-2z=14 The normal vector to a plane ax+by+cz=d is a,b,c Hence, the normal…

Q: Find an equation of the plane. The plane that passes through the point (2, 4, 5) and contains the…

A: