Consider the plane 9x + 3y + z = 27. (a) Write down the point at which the given plane intersects the x-axis. (b) Write down the point at which the given plane intersects the y-axis. (c) Find an equation of the line of intersection of the given plane and the xy-plane.  d) Set up (but do not evaluate) an iterated triple integral of the form  dz dy dx that represents the volume of the solid enclosed by the given plane and the planes x = 0, y = 0, z = 0

Q: Find a parametrization of the line in which the planes x- 2y - 2z = 3 and -3x + 3y + 3z = -6…

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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+2y-z = 3. 0=0

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Q: (x² + xy) dx + (y² - xy) dy; C: the line y = x from the origin to the point (2, 2).

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Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

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Q: Find a scalar equation of the plane containing the line x = 4+ 5t, y = 5+3t and z = 6+ 4t the point…

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Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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Q: Consider the three following points of R'. A = (0, 2, 2) B = (1, 1, 1) C = (-1, 1,2) (a) Find the…

A: The scalar equation of a plane is of the form: ax+by+cz+d=0, where a, b, c ,d are constants. The…

Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

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: Find the points on the surface 1x² + 1y² + 3x² = 1 at which the tangent plane is parallel to the…

A: We know that two planes are parallel if their normal vector are parallel. That is their, gradient…

Q: Consider the plane x-y-z-8= 0. Find the point in this plane closest to the point (1, 0, 1).

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Q: Give a acalar equation for a plane at distance 6 from the plane P with equation x+2y+2z = 5. 0-0

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Q: I= -1- 4t Consider the lines l :{y = 4+ 4t z = 7+ 8t (r= 4+3s , teR and l2:{ y = 1-s , s€ R. : = 5+…

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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: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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Q: 2. Determine the vector-function curve of intersection of the plane given by the equation x = 9/2…

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Q: Which of these is the correct parametrization of the line connecting (1,2,5) and (0,3,– 1)? A. x =…

A: We know that parametrization of the line connecting pointsx1,y1,z1,x2,y2,z2 is given by x=x1+tx2-x1;…

Q: The domain is the entire xy-plane.

A: Domain -Domain constitutes only the values of x on which the function is defined.

Q: The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations…

A: Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…