Prove that the parallels through to the origin to the binormals of the helix     r= (acost,asint,kt) Lie on the right circular cone a^2(x^2+y^2)=k^2z^2

Q: AP is perpendicular to PB, where A is the vertex of the parabola y^2 = 4x and P is on the parabola.…

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Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: Which point is closest to the yz-plane? ? What is the distance from the yz-plane to this point?

A: The distance of a point from the yz-plane is given by the x coordinate of the point. Because, the x…

Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

Q: Find foF dr where C is a circle of radius 3 in the plane x+y+z= 8, centered at (1, 3, 4) and…

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Q: Verify Green's Theorem where F1=y^2-7y , F2=2xy+2x and the curve C is a circle x^2+y^2=1

A: Given: F1=y2-7y , F2=2xy+2x and C is a circle i.e., x2+y2=1 As, we have:…

Q: Solve for the distance between the point P(0,0,0,0) and the plane w + x + y + z = 3 in R^4.

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Q: - )and (,- The points of intersection between the Curves r= 3cose and r= 2- cose are: A))and (…

A: Let's find intersections points.

Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: | Let w=z² Find the image of the first quadrant in Z-Plane 2

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Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

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Q: show that a=(2x^2+8xy^2z)i+(3x^3y-3xy)j-(4y^2z^2+2x^3z)k is not a solenoidal but b=(xyz^2.A) is…

A: Given:A=2x2+8xy2zi+3x3y-3xyj-4y2z2+2x3zk To check solenoid we will check ∇.A=0 or not…

Q: If a line segment AM-a moves in the plane XOY remaining parallel to OX so that the left endpoint A…

A: Sol:- Let the center of the circle be at point O(0,0), and let the left endpoint of the line segment…

Q: Find the locus of the point of intersection of the tangents to the circl x2 + y2 = a2 mhoco at…

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Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

A: A = JBJ-1 A = span { v1, v2}  And span {v1 , v4} and span { v5}  v1 , v2 , v3 , v4 , v5 having eigen…

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

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Q: 5. Find the distance from the point (4, -3, 6) to the plane *-2y+z=1

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