) Prove part (a) assuming that the domain D enclosed by the simple closed curve C with positive orientation is of the form D={(x,y) | a ≤ y ≤ b, g(y) ≤x≤ 92(9)}, where gi(y), 92(y) are continuous functions, and a, b are some real numbers.

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: 2. (§1.1) Sketch the following set of points in the x-y plane. {(x, y) = R²: (y - x²) (y + x²) < 0}.

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Q: _et a₁ = -1 a₂= -7 -7 3 and b = 3 -15 h For what value(s) of his b in the plane spanned by a, and a

A: If b is in the plane spanned by a1 and a2 then b can be written as linear combination of  a1 and a2…

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: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

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Q: Postulate 12 states that if two points lie in a plane, the line that contains them lies in the…

A: We need to determine whether the given statement is true or false. Postulate 12 states that if two…

Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

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Q: Q4-Find the Cartesian equation of the line that passes through the point (-3, 2,-1) and is parallel…

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Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: Q7) The equation of the plane contains the points (3,2,1), (2,1,-1) and (-1,3,2) is 2x-9y-5z=16. * F

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Q: Answer the questions in detalied steps and show work. (7 and 8)

A: Step 1: Step 2:   Take x-axis and y-axis                 they intersect at (0,0) in two-space and…

Q: What are the coordinate planes in three-dimensional space? How are they drawn?

A: The Cartesian coordinate system is used to describe three-dimensional space which consists of an…

Q: Let a, 1 1 -7 -7 3 and b = 3 15 h For what value(s) of h is b in the plane spanned by a, and a₂?

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Q: Let a be a real number such that a opposit to 0 . An equation of the plane passing through A…

A: Given data:- Plane passing through the points, Aa,-a,-aBa,0,2aC-a,-a,-5a

Q: Q3// :- Write an equation for the plane containing points P=(1,1,-2),Q=(0,2,1), and R=(-1,-1,0)

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Q: If 6 0, can the solution set of Ax = be a plane through the origin? Defend your response. Your work…

A: Given condation b is not equal to zero. And equation: Ax=b We have to check b doesn't equal to zero…

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: (222) Determine the x-, y- and z-intercepts of the plane 3x-8y-8z +24=0

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Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: nt of intersectic -6 y + 8 = 3 O) カー

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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: (a) Determine all real values of b such that the set of all linear combination of u = (b, 2) and v =…

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