Multiple choice question Given point 1 345 cm point 2 024

Multiple choice question:

Given point 1 = (3,4,-5) cm, point 2 = (0,2,4) cm and point 3 = (-1,0,0) cm determine a direction orthogonal to a plane that contains all three of these points

a) 0.722i - 0.624j + 0.119k

b) 0.722i+0.624j-0.119k

c) Both A and B are correct

d) None of the above

Solution

equation of the plane that passes through these three point is

| x-3 y-4 z+5 |
| -3 -2 9 | = (-10+36) (x-3) - (y-4)(-15+36) + (z+5)(12-8) = 26x -21y +4z -78 +84+20 => 26x-21y+4z+26=0
| -4 -4 5 |

Hence equation of the plane is = 26x-21y+4z= -26 but we know that sqrt(26²+ 21²+ 4²) = 33.66
Thus the given plane can be written as 26/33.66 x -21/33.66 y + 4/33.66 z = -26/33.66
Thus the plane becomes = 0.722x - 0.624y +0.119z = k so compare the coefficients (which are direction cosines of the normal to the plane) with the given options

A option is the right answer