Find an equation for the tangent plane to at .

Question

Find an equation for the tangent plane to  at  .

Quizplus · Accepted Answer

To find the equation of the tangent plane to a surface at a point, we need to find the gradient vector of the surface at that point. For the given surface, 11ead0bc_8db9_1fc3_99a0_cd58a7100622_TB6988_11, the gradient vector is: grad(11ead0bc_8db9_1fc3_99a0_cd58a7100622_TB6988_11) = <2x, 2y, 2z> At the point 11ead0bc_8db9_1fc4_99a0_871157c33a8c_TB6988_11, the coordinates are x=1, y=2, z=3. So the gradient vector at that point is: grad(11ead0bc_8db9_1fc3_99a0_cd58a7100622_TB6988_11)(1,2,3) = <2, 4, 6> Now, we can use the point-normal form of the equation of a plane to find the equation of the tangent plane. The equation is: 2(x-1) + 4(y-2) + 6(z-3) = 0 Simplifying, we get: 2x + 4y + 6z - 26 = 0 So the answer is choice D, 11ead0bc_8db9_46d8_99a0_2d82ffdcc697_TB6988_11.

Find an Equation for the Tangent Plane to at