Calculus 3- 12.5Planesinthree-space

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1.

Write an equation of the plane with normal vector n= (4, -3, -8) passing through the point (2, -9, -8) in scalar form = 198The plane whose points satisfy the equation 3(x + 6) - 8(y - 13) + 5z = 0 has many vectors which are normal to it. One of those normal vectors is n = help (vectors)Find the equation of the plane which passes through O and is parallel to z - (3x + 5y) = 3 y + z =Find an equation of the plane through the three points given: P = (33030) :Q = (41 _21_1)1R =(41_212) = 18 Determine whether or not the lines have a single point of intersection. If they do, give an equation of a plane containing them. 1-101) 2 (131:, 6t 7 1,6t i 6) and r2(t) = (t i 13, it + 12,t i 19) (Use symbolic notation and fractions where needed. Enter "DNE" if two lines do not intersect.) Equation of a plane: Determine whether or not the point lies on the line. If it does not, give an equation of a plane containing the point and the line. (13, -16, -9) and r(t) = (1 - 6t, 6t - 7, t - 7) (Use symbolic notation and fractions where needed. Enter "DNE" if the point doesn't lie on the line.) Equation of a plane