Loading [MathJax]/jax/output/HTML-CSS/jax.js


1)

The equation of the  plane passing through the points with position vectors A(2ˆi+6ˆj6ˆk), B(3ˆi+10ˆj9ˆk)  and C(5ˆi6ˆk)  is 


A) r.(2ˆiˆj2ˆk)=2

B) r.(ˆi2ˆjˆk)=1

C) r.(2ˆi+ˆj2ˆk)=3

D) r.(ˆi+2ˆj2ˆk)=3

Answer:

Option A

Explanation:

Equation of plane passing through any three  given point is 

[xx1yy1zz1x2x1y2y1z2z1x3x1y3y1z3z1]

   Points are (-2,6,-6),(-3,10,-9) and (-5,0,-6)

    [x+2y6z+6143360]=0

  (x+2)(018)(y6)(09)+(z+6)(6+12)=0

    18(x+2)+9(y6)+18(z+6)=0

     18x+9y+18z=36+54108

    2ˆi+ˆj+2ˆk=2

   2ˆiˆj2ˆk=2

    r.(2ˆiˆj2ˆk)=2