Question

Consider the family of planes $x+y+z=c$ where $c$ is a parameter intersecting the ccordinate axes at $P,Q,R$ and $\alpha ,\beta ,\gamma$ are the angles made by each member of this family with positive $x,y$ and $z$ axis. Which of the following interpretations hold good for this family.

• A. each member of this family is equally inclined with the coordinate axes
• B. ${\sin }^2\alpha +{\sin }^2\beta {\sin }^2\gamma =1$
• C. ${\cos }^2\alpha +{\cos }^2\beta {\cos }^2\gamma =2$
• D. for $c=3$ area of the triangle $PQR$ is $3\sqrt{3}$ sq. units.

Answer 1

The correct option is A each member of this family is equally inclined with the coordinate axes

Consider the family of planes $x+y+z=c$

where $c$ is a parameter intersecting the ccordinate axes at $P,Q,R$

and $\alpha ,\beta ,\gamma$ are the angles made by each member of this family with positive $x,y$ and $z$ axis.

$\therefore$ each member of this family is equally inclined with the coordinate axes