The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the equations - O a) None of these O b) 4x – y + 2z = -11 and (x, y, z) = (2, –1, 1) + t(2, –1,1) | c) 4.x + y+ 2z = 9 and (x, y, z) = (2,-1, 1) + t(4, 1, 2) O d) 4x – y+ 2z = 11 and (x, y, z) = (2, –1, 1) + t(4, –1, 2) -

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: 2) = ( (x, y, z) =

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Q: Evaluate [(y² - 4xy, 2xy - 2x²). C where C is the line from (0, 0) to (1,5) followed by the line…

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Q: An equation for the tangent plane to the surface : = (xty at the point P(1, 1, 4) is a) 8x + 8y -: =…

A: Equation of a tangent to the surface z=f(x,y) at point (a,b,f(a,b)) is given by…

Q: 4) Show that the surfaces 3X² + 2Y²+Z² = 9 and x² + y² + Z²-8X-6Y-8Z + 24 = 0 have a common tangent…

A: We have to prove both surfaces have common tangent at P(1,1,2).

Q: Find an equation of the tangent plane to the surface z2 +2y + 2 = 175 at the point (5, -5, 10). O 10…

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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: Suppose that the plane tangent to the surface z = f(x, y) at (-4, 2, 5) has equation z + 5x + 4y =…

A: From the equation of tangent, we can derive: z = -(7 + 5x + 4y) Hence,

Q: aces x2 + y2 pint (2, -1, 2)

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Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

Q: you know that a sphere has the equation of  x^2 + y^2 +z^2 -6x +4z =3 are the following points…

A: The equation of sphere is:-Now add 9 and 4 both side:-

Q: An equation of the straight line normal to surface x2 - y3 + z = 8 at the point P(2, -1, 3) on the…

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Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

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Q: 2. Obtain an equation for a plane 7 that includes straight line(2"--5) and point(-2,1,1).

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Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t

A: The plane given by x + y + 2z = 0 and the line given by x = 2 + t;  y = 1 - 2t ;  z = 3 + t To find…

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: 19. Find the distance from the point (3, -2,7) to the plane 4x – 6y + z = 5. Show all necessary work…

A: A detailed solution is given below.

Q: 11) A point on the surface 2x + y? + z? = 4 at which the tangent plane is parallel to the plane x -…

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