Consider the following diagram which indicates relative positions only (lengths are not to scale): В A D Suppose that C has coordinates (2, 2,0) and B has coordinates (0, 1, 3), and O is the origin. Using orthogonal projections, determine the co- ordinates of D.

Q: Calculate fo(7x + 6y) i + (4x + 7y) j) dr where C is the circular path with center (a, b) and radius…

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A: The coordinate plane looks as below:

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A: r(t) = t i + t2 k We need to find the plane of the curve located in?

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A: From a point S(x0,y0,z0) to the plane M = ax+by+cz+d=0 Let S1=x1,y1z1 be any point in the given…

Q: Find the moving tri hedral of f R CE) = t, 2E> at %3D

A: This is a problem of differential Geometry.

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Q: Use Eq. (5) to find the point P nearest to Q = (2, 1, 2) on the plane x+y+z=l.

A: Consider the provided information, Find the point P. The normal vector to the plane is 1,1,1. And…

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A: Find the condition for the given points to be collinear.

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A: If be a positively oriented,  closed curve  enclosing the region D Then for a vector field F→=P,Q…

Q: d) If S is projected onto the x - y plane, what is the shape of the resulting projection?

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Q: If S is projected onto the x – y plane, what is the shape of the resulting projection?

A: Idea: if we project the surface in xy- plane z=0. if we substitute z=0 in surface equation we get…

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Q: Match the surfaces (a)-(e) with the contour diagrams (1)-(V, (M)

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A: First obtain the plane that parallel to the xz-plane containing the point (1, 2, 3).…

Q: 21. Find the equation of the perpendicular bisector of the segment joining (1,2) and (5,4) (Figure…

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Q: Show that the curve a(t) = (t,4,²) lies in a plane and find the equation of this plane.

A: Solution:- αt=t,1+tt,1-t2t t,1t+1,1t-t=x,y,z It is clear that, t-1t-1+1t-t=x-y+z x-y+z=-1

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A: We have to name the plane which intersects in FG,

Q: The notation (x, y) → (-x, y) defines a reflection on the coordinate plane, O True O False

A: Solving the problem by helping of a point.

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A: If m1 = tangent at point (x,y) and     m2 = tangent at point (x,y) then Orthogonal conditions is…

Q: What is the projection of r(t) = ti + t4j + etk onto the xz-plane?

A: Given: r(t)= ti+t4j+etk

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A: Given: R=-4,4S=0,-2T=-3,-1

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A: In this question, we have f(z)=x2+iy2 To find the line integral from  z1=2i  to z2=2+4i

Q: Consider the line L(t)=⟨4t−1,2−5t,−3−4t⟩. Is L parallel, perpendicular, or neither to the plane…

A: Lt=<4t-1 , 2-5t , -3-4t >Direction ratio of Lt=< 4 , -5 , -4 >Normal vector to given…

Q: Consider the following. Z = 4 Sketch a graph of the plane.

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Q: Evaluate f 3z2dz over C, where C is the upper half circle |z – connects points O and 1+i. -글히 %3D플…

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Q: Show that the curve a(t) = (t, , ) lies in a plane and find the equation of this plane.

A: For all 't' , we have α'(t) = 1 , -1t2 ,-1 - 1t2α"(t) = 0 , 2t3 , 2t3 Now  α'(t) × α"(t) = 2t3 ,…

Q: | the parametric equatioin for e line segment between a7) and (3,3)

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Q: Suppose we have: u = and v = . Based on their relative positions in the xy-plane, in which…

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Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: In ARST, SV bisects y ZRST. Find the coordinates of point T in terms of a. S (a, a) 2a T?, ?) V (2,…

A: Given that, Let ∠TSV=θ and ∠VSR=θ(∵SV is angle bisector)

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A: Let the given point be (x0, y0, z0), to find the osculating plane find the cross product of the…

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Q: Consider the projection from the origin of the straight line y + x = 2 on a straight line y + 2x =…

A: Graph formed by

Q: -1. Through (1,5, 2) perpendicular to 37 – J + 4k .

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Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

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Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

Q: Find b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

Q: (2, 1) is the midpoint of AB, in which A has coordinates (8, 10). Find the coordinates of B.

A: given: (2,1) is the mid point of AB. the coordinates of A are (8,10) we have to find the coordinates…

Q: (A) Find the unique point P on the y-axis which is on both planes. (–, ,

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Prove that the perpendicular distance from the point P(xo, Yo, 20) to the plane with equation ar +…

A: Here we use the distance formula between two points.

Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

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Q: T 1) Reflect quadrilateral ABCD across the y-ar reflection on the coordinate plane to the right. new…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let h VI and y: 8 For what value(s) of h, is y in the plane generated by vị and v2?

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Q: Consider AB in the coordinate plane below. 10 7 5 4 3. 2 A B 6 7 89 10 10-9 -8 -7 -6 -5 -4 -3 -2 -1…

A: i am going to solve the given problem by using some simple geometry to get the required result.

Q: Let f(z) = x² + iy where x and y are the real and imaginary parts, respectively of z and C is a…

A: ii