Question 384 of 521MediumMCQ
The distance of the point (1,−5,9) from the plane x−y+z=5 measured along the straight line x=y=z is Solutions · 1
Official solution
\[e{q^n}\,\,\] of \[\,\,PO:\,\,\] \[{{x - 1} \over 1} = {{y + 5} \over 1} = {{z - 9} \over 1} = \lambda \]
\[ \Rightarrow x = \lambda + 1;\,\,y = \lambda - 5;\,\,z = \lambda + 9\]
Putting these in eqn of plane :-
\[\lambda + 1 - \lambda + 5 + \lambda + 9 = 5\]
\[ \Rightarrow \lambda = - 10\]
\[ \Rightarrow O\] is \[\left( { - 9, - 15, - 1} \right)\]
\[ \Rightarrow \] \[\,\,\,\] Distance \[OP = 10\sqrt 3 .\] Answer the question to unlock