zdx + (х — 2у)dy + zdz

Q: Show that the equation of a circle passing through the origin and having intercepts a and b on real…

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Q: Find the x-coordinate on the graph of f (x) = x ³ – 12 x where the tangent is horizontal. A) 1,-1 B)…

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Q: Evaluate fr (y-x-3x²i)dz where C is the straight line from z = = 0 to z = 1 + i. 2+i

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Q: the graph of the function y = -3x² + 2x-5 intersects the Oy axis at the ordinate point: a) 2 b) 5 c)…

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Q: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: Find all points with coordinates of the form (a, a) that are a distance 3 from P(-2, 1).

A: Given: P(-2,1) and distance is 3. To find the other coordinate point.

Q: (0,1,1) to the line of intersection of the planes : x + 2y + z = 1 x - y + 2z = -8

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Q: What is the image of a horizontal line y = k € R under the mapping W = 2²?

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Q: Let a,= 4 az = - 21 and b = - 12 For what value(s) of h is b in the plane spanned by a, and a,? 1 2…

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Q: 1 -2 4 17. Let a 4 a2 -3 and b : For what 7 value(s) of h is b in the plane spanned by aj and a2?

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Q: how the condition that the curves a+b=1 and d+b'

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Q: Use the applet to translate quadrilateral ABCD 2 units left to create quadrilateral A'B'C'D', then…

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Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: Consider the points P = (1,2,0), Q = (0,1,2), and R=(2,0,1). Let A be an arbitrary point in…

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Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: 0- Draw a sketch of the Plane of 4x-tyt22-9=0

A: Solution

Q: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

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Q: 3. Show the parametric form of the line that passes through points A(3, 6, 1) and B(2,10, 5) Compute…

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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: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: 3) Find the distances: a. Between ₁ = (3 + t, −2+ 3t, -t) and 1₂ = (1 + 2t, t, 5+ 4t). b. Between…

A: "Since you have posted multiple questions, we will provide the solution only to the first question…

Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

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Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

Q: b) Find the intersection point of the line Lix-1.y-3+t, z4+2t with xz-plane.

A: Here we have given equation of line and we have to find the point of intersection of given line with…

Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: Let P(-4, 1, -3) be a point that is not on the line L . Let the line L pass-through points Q and R…

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Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

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Q: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

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Q: Are these points collinear? a) A(-1, - 2), B(3, 2), and C(5, 5) b) D(a, c-d), E(b, c), and F(2b - -…

A: If the points are colinear then the slope of the lines making with the points are same. Find the…