3) Suppose plane P, contains the points A(5,0, –1), B(2,3, 2), and C(-2, 1, –4), and assume P, is the tangent plane to a function z = f(x, y) at the point C. Find a possible formula for f (x, y) that is NOT linear (there are many correct answers!).

Q: Find an equation of the line through (-2, 5, 3) that is perpendicular to both u = (1, 1, 2) and the…

A:

Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

A:

Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

A:

Q: Let Lz be the line passing through the point P-(10, 1. –10) with direction vector d--2, -2, 3]", and…

A: We will use formula for the shortest distance.

Q: Find values of a and c such that the tangent to y = ax2 + 12x + c is horizontal at the point (2,5)

A: Tangent is horizontal where derivative is zero

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

A:

Q: In the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2,…

A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…