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: 32. Find the equation of a plane through the origin and per- pendicular to x – y+ z = 5 and 2x + y–…

A: Note- According to Bartleby guidelines, we are supposed to do only one question. If you want more to…

Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

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: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: x-2 z+4 • Let L:*²=+3 = 2²+ and M: 2x - 3y +z = 6 are line and 3 2 5 plane and let P be the…

A: We have to find the equation of line

Q: Evaluate ▼ (x² y + x y z²) ·dr where C is the line segment from ( 1, – 1,0) to (2,1,3 Select one: a.…

A: Given integral is

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: line through the variable point A(k+1,2k) meets the lines 7x+y-16=0 ,5x-y-8=0,x-5y+8=0 at…

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Q: Give an example of (v1, v2, v3) and (w1, w2, w3) independent se- quences in the R“ such that…

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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: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: Give an example of (v1, v2, v3) and (w1,w2, w3) independent se- quences in the Rº such that…

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Q: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

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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: 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: Find √x²ds ds along the line of intersection of the two planes x-y+z=0 and x+y+2z=0, from origin to…

A: The two given planes are x-y+z=0 and x+y+2z=0.

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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Q: Let C be the rectangle in the xy-plane with vertices (0,0), (1,0), (0, 2) and (1, 2), and let F(r,…

A: