JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    If from a point  \[P(a,b,c)\] perpendiculars \[PA\] and \[PB\]are drawn to yz and zx planes, then the equation of the plane \[OAB\] is

    A)            \[bcx+cay+abz=0\]

    B)            \[bcx+cay-abz=0\]

    C)            \[bcx-cay+abz=0\]

    D)            \[-bcx+cay+abz=0\]

    Correct Answer: B

    Solution :

               \[A\,(0,\,\,b,\,\,c)\] in yz-plane and \[B\,(a,\,\,0,\,\,c)\] in zx-plane. Plane through O is \[px+qy+rz=0.\] It passes through A and B.            \[\therefore \,\,0p+qb+rc=0\] and \[pa+0q+rc=0\]            \[\Rightarrow \,\,\frac{p}{bc}=\frac{q}{ca}=\frac{r}{-ab}=k\]                    \[\Rightarrow \,\,p=bck,\,\,q=cak\] and \[r=-abk.\]                    Hence required plane is \[bcx+cay-abz=0\].

You need to login to perform this action.
You will be redirected in 3 sec spinner