/ Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

Q: Find the distance between the planes 5x − 3y + z = 2 and 5x − 3y + z = −3

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Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4

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Q: The equation of the area of the plane region bounded by y = x^3 and the lines x = 1 and y =0 is…

A: Detail solution written below

Q: Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 −…

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Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Calculate the distance from the point (4,−2,7) to the plane x−3y+5z=−8.

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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: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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Q: 2. Find the distance between the given parallel planes. 2x +y+ 2z = 8 and 4x +2y + 4z +5 = 0

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: Calculate the distance from point s(10, -8, 10) to the plane 2x + 2y + z = 4 O 10 O 10 의 ~m 의 29

A: Given query is to find the distance between the plane and point. The given point is S(10, -8, 10)…

Q: At what point does the line: L: x=-1, y= 10 + 31, z= 4 +3t im plane 1:x- 2y + 5z + 16 = 0?

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Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: Determine equation of tnagent line to the common curve of 2 surfaces w/ equations: z = x? + y – 2xy…

A: follow next step

Q: Find the distance between the parallel planes – 2x + y + z = 0 and Edit 10x – 5y – 5z – 26 = 0. -

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Q: Picture attached. Thanks in advance!

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Q: Find the distance between these two planes x + 2y –' 2z = 3 and 2x + 4y - 4z = 7.

A: Devide the equation of 2nd plane by 2 .we get that both planes are parallel so just apply formula…

Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Find the distance from the point (2, 0, 0) to the plane x + 2y + 2z = 0.

A: Given a point, (2, 0, 0) and the equation of the plane x + 2y + 2z = 0.

Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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Q: Find the distance from the point (3, 4, -1) to the plane lr 3y +2z = 5.

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Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4.

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Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

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Q: Find the distance from the line x = 2 + 1, y = 1 + 1, z = -(1/2) – (1/2)t to the plane x + 2y + 6z =…

A: The equation of line: x=2+t,  y=1+t,  z=-12-12tTherefore:x-21=y-11=z+12-12 Equation of the plane is:…

Q: Show that the area of the plane region bounded by the curves,  x - y =7   and    x= 2y² - y + 3…

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Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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Q: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

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Q: find the slope of the tangent to the curve of intersection of the surface 3z=√36-9x²-4y² and the…

A: Consider the surface 3z=36-9x2-4y2and the plane x=1 at the point 1,-2,113.The objective is to find…

Q: Find the distance from the point S(0,0,0) to the plane 20x+10y+5z=70 (approxmate to two decimal…

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Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

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Q: Find the distance between the point (3, −2, 4) and the plane 2x − 5y + z = 10.

A: Given: The equation of a plane is 2x-5y+z=10. To determine: The distance between the point 3,-2,4…

Q: Find √x²ds ds along the line of intersection of the two planes x-y+z=0 and x+y+2z=0, from origin to…

A: The two given planes are x-y+z=0 and x+y+2z=0.

Q: Find the distances (a) Between l1 = (2+ 2t, –1+t, -3t) and l2 = (4, -5 – 3t, 1+ 4t) (b) Between the…

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Q: Find the distance between the parallel planes −3x+y+2z=−4 and 6x−2y−4z=1?

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Q: Find the distance from the point (0,8,9) to the plane – 2y + 3z = 11.

A: In this question, we will find the distance from the given point to the given plane.

Q: Find the point on the plane 8x - y + 8z = 80 nearest the origin. (x, y, z) =

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Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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Q: find the slope of the tangent to the curve of intersection between 6z=3squareroot(20-x^2) and the…

A: the cylinder equation is given by  and the plane is given by  We want to define each variable in…

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: Find the distance between the planes  5x − 3y + z = 5  and  5x − 3y + z = −9.

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…

Q: Find the plane determined by the intersecting lines. y = 2+ 4t L1 x= - 1+2t z = 1- 2t L2 x= 1-4s y =…

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Q: Find the angle between the line 2 x+v3 : = z + 1 and the plane vZx + y + z – 2 = 0.

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Q: Find the distance from the point to the plane. (3, 0, 10), 2.x + 3y + z = 2

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