In V=R3 Let W1 be the xy-plane and  let W2 be the z-zxis:             W1={(x,y,0):x,y∈R}  and      W2={(0,0,z):z∈R}  Show that

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: Let Z = (1, 1, 2) be a point in R³. Find the closest point to Z tha lies on the plane give by -x+y-z…

A: The normal vector to the plane is <-1, 1, -1>. The point you seek would have to be some…

Q: Determine the intersection if any between the line L₁: [x, y, z] = [3, 2, − 5] + r[0, 1, 4] and the…

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Q: Show that the line [x, y, z]= [5,-1,3]+[4,-5,2] lies on the planes 3x+2y-z = 10 and 7x+4y-4z=19.

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Q: Graph: y> z – 1 y

A: We need to graph the sketch of the curve given by  y>14x-1y<-4x+1. To draw the graph, first,…

Q: Consider the function f: N→ N defined as f(n) = 2n-1. Are the following true or false?

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: The line of intersection of the planes x + y + z = 0 and x - y = 0 is

A: The given planes are..Find the equation of the line in parametric form.

Q: 2. Find a vector that is perpendicular to the surface x² + y² + z² = xyz + 8 at the point (1,2,3).

A: Given that x²+y²+z²=xyz+8 At (1,2,3)

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Theorem to…

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Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

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Q: ind the point of intersection for the lines v(t) = (-5, - 8, -6)t + (− 1, 3, 1) and (u) = (6, 6, 2)u…

A: First we find value of parameters u and t .

Q: x(t) Find a plane containing the point (6,-4,4) and the line y(t) z(t) 3 + 3t -3+ t 6 + 3t

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