Question
14. Find an equation of the plane that passes through the point (-1,-3,2) that contains the line x=-1-2,y=4t, z = 2+1 15. Find the parametric equations for the line of intersection of the planes 2x + 5 z +3 = 0 and x-3y+z+2-0 16. Find the distance between the point (1.0,1) and the plane x-2y-2z1. 17. Let ar(-4,2,0) and b= (1,1,1). Find the projection of b onto a. 18. Rewrite i, , frorn spherical coordinates into cylindrical and rectangular coordinates 19. Find an arc length parametrization of the curve that has the same orientation as the given curve and for which the reference point corresponds to t = 0: 3'4 20. Find T(1) and N(t) at the given point: r(t)-(t2-1)it, t=1.
Explanation / Answer
14. equation of plane
x- x1/a = y-y1/b = z-z1/c = k
(x1,y1,z1) = (-1,-3,2)
x +1 /a = y+ 3 /b = z- 2/ c = k
x +1 = -2t
y = 4t
z = 2+ t
eq of form
put (x,y,z) = (-1,-3,2)
x + 1/ 1 = y/0.75 = z/1
16.