EXERCISE 1 (8/32) (a) (2 points) Find the cartesian equation of the plane passing through P= (1,0,2) and orthogonal to <

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Exercise 1 8 32 A 2 Points Find The Cartesian Equation Of The Plane Passing Through P 1 0 2 And Orthogonal To 1 (45.23 KiB) Viewed 15 times

EXERCISE 1 (8/32) (a) (2 points) Find the cartesian equation of the plane passing through P= (1,0,2) and orthogonal to <1,2,-1>. (b) (3 points) Determine the parametric equation of the straight line passing through Q=(1,0,2) and P (1,0,1). Find the points belonging to the line whose distance from Q is 2. (c) (3 points) Let P (1,0,0), P (0,1,0) and Ps= (0,0,1). Compute the area of the triangle with vertices P₁, P₂, P. EXERCISE 2 (8/32). (a) points) Draw 7₁(t)=<t,tcost, tsint> with 0 < t < 4. • Let 7'z(t) =< t, 2t cost, t, tsinf>. What kind of geometrie transformation do we need to apply to 7₁(t) so to obtain 72(t)? (b) (6 points) Let A= 12 6 14 12 3 8 12 24 By employing the Rouché - Capelli theorem discuss the solvability of the linear system Ar b. Specify if the solution exists unique. In case of existence, determine the solution(s) employing the Gaussian Elimination method.