Please answer #1-6 and show work

1. Three vectors are given: a (1, 0, 2) , b (0, 1, 3) , c (5, 1, -1) . Find two vectors x and y such that: (a) c = x+ , (b) x is in the plane( a, b ), (c) y is perpendicular to this plane. 2. A plane is determined by the three points P, (1, 0, 2), P2 (2, 1, 0), P; (1, 2, 3) and a line is determined by the two points P, (1, 1, 1), PS (6, 0, 3). Which of the following is true: (a) the line is in the plane, (b) the line is parallel to the plane, (c) the line is intersecting the plane (and find the coordinates of the crossing point). 3. Find the equation of the tangent plane to the surface x -2y' + 3z' =2 at the point Po ( 1, 1, 1 ) . 4. Find the Taylor polynomials of degree one T, (x, y ) and of degree two T2 (x, y ) for the function f (x, y) = In(2x+ y) at the point Po (Xo, yo ) = Po (1, 1). For the point P(x, y) = P(1.1, 0.9) find the three decimals (round with respect to the sixth digit after the decimal point): T, (1.1, 0.9), T2 (1.1, 0.9), f (1.1, 0.9). 5. Find the local extremums / saddle points of the function f (x, y) = xy txy txty. 6. Find the point on the plane x- 2y + 2z + 4=0 that is on the shortest distance from the point Po ( 3, 4, 5 )