Let the surface xz – yz³ + yz? = 2, then - the equation of the tangent plane to the surface at the point (2, –1, 1) is: O x – y + 3z = 5 | O x – 3z = 5 O x + 3z = 5 O x + y + 3z = 5 O y+3z = 5

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

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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: Consider the surface O3z+3y-2z=0 O 34z + 7y-12z = 0 O 3x+3y-2z=147 What is the equation of the…

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Q: Find the equation of the tangent line to the trace y-3 of the quardic surface defined by 9x² + 2y²…

A: We have to find the equation of the tangent line to the trace y=3 of the quardic surface defined by…

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Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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Q: The surface z = x² - y² and the surface ryz = -30 intersect along a curve in R³. Find a vector…

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Q: The slope of the surface z = ry² in the r-direction at the point (2,3) is slope of this surface in…

A: The slopes of the surface: z=f(x, y) in the x, y directions at x0, y0 are fxx0, y0, fyx0, y0.

Q: Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2,…

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Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

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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: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4…

A: This is the problem from the vector algebra and 3D geometry.

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: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given: