Equation of a plane passing through ^i+^j+^k parallel to both ^i+^j and ^j+^k can be given by
¯r.(^i−^j+^k)=1
We know equation of plane passing through ¯a perpendicular to ^nis (r−¯a).^n=0
Here, a=^i+^j+^k
How to get ^n?
We can see ^n is perpendicular to both ^i+^j and ^j+^k i.e., along (^i+^j)×(^j+^k).
∴(^i+^j)×(^j+^k)=∣∣ ∣ ∣∣^i^j^k110011∣∣ ∣ ∣∣=^i(1)−^j(1)+^k(1)=^i−^j+^k
⇒ ^n=^i−^j+^k√12+12+12=^i−^j+^k√3∴ equation of plane⇒(¯r−(^i+^j+^k)).^n=0
¯r.(^i−^j+^k√3)=12−12+12√3=1√3∴¯r.(^i−^j+^k)=1