Find the envelope of the plane lx + my + nz = p, a²12 + b²m² + 2np = 0

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: which of the toihts PC6,L3), Q (-5,-1,4), and R(0,3,8)15 c losest to the X2-Plane? which paint lies…

A: A point in 3D has (x,y,z) coordinates. A point on XY plane has (x,y,0) coordinates i.e. z=0 A point…

Q: Find the distance from the point (7, -14, -21) to the plane:  2x - 3y - 6z = 1

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Q: b) Use the idea in part (a) to determine an explicit one-to-one correspondence between zt and the…

A: as you asked only the solution for (b) , the solution of the part (b) is given below...

Q: Find the length of the diagonals of rectangle WXYZ 

A: Solution The objective is to find the lengths of the diagonals of rectangle. By Rectangle Diagonals…

Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: Determine the line of intersection between the following planes 12. 5x+2y-7= 9 and -2x+8y +9= = 3.

A: Given: The planes are 5x+2y-7z=9 and -2x+8y+9z=3 To find the line of intersection of the given…

Q: Enter any point on the plane 6x + 5y + 5z = 18

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Q: ,1), (2, 2), (1, 3), (4, 1), (3, 2), (2, 3), (1,4), (5, 1), .... Show that this constitutes a proof…

A: We will answer the first question only as we don't answer multiple questions at a time. Please…

Q: Translate quadrilateral BDFH using the rule (x, y) (x+ 6, y- 10) and label the image D B

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Q: What is the direction perpendicular to the plane containing F₁ and F₂? F₁ = (11î+ 4ĵ- k) N F₂ =…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: What is the center of x² + y² – 6x = -4y + 68?

A: given equation of circle  x2 +y2-6x=-4y+68  x2+y2-6x+4y-68=0 Now compare with x2+y2+2gx+2fy+c=0…

Q: The equation x² + 14x + y² – 8y +z2 +10z = – 65 represents a sphere whose center is (-7,4, – 5) |

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Q: Find the dot product of ū = (3,-2) and v = (5,-7). Select one: -1 V29 29 (8,-9)

A: Consider the vectors u→=3,−2v→=5,−7

Q: Which point(s) lie in the plane 2x + 3y + 4z = 24? a) (0, 0, 6) c) (4, 4, 1) b) (0, 3, 4) d) (-2, 6,…

A: Given: 2x+3y+4z=24 For finding which point lie on given equation of plane, we put each point on…

Q: Find the area of the parallelogram whose vertices are: A(0,0,0) B(5,2,6) C(9,-1,6) D(4,-3,0)

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Q: Find the area of the parallelogram with vertices: P(0,0,0), Q(-4,-5,4), R(-4,-3,6), S(-8,-8,10). 0

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