Let $$P1$$ denote the equation of a plane to which the vector (i^+j^) is normal and which contains the line whose equation r→$$=i^+j^+k^+$$λ(i^$$−$$j^$$−$$k^) and $$P2$$ denote the equation of the plane containing the line L and a point with position vector $$j^$$ Which of the following holds good?

Question

Let $$P1$$ denote the equation of a plane to which the vector (i^+j^)  is normal and which contains the line whose equation  r→$$=i^+j^+k^+$$λ(i^$$−$$j^$$−$$k^) and $$P2$$ denote the equation of the plane containing the line L and a point with position vector $$j^$$ Which of the following holds good?

Infinity Learn · Accepted Answer

Plane $$P1$$, contains the line r→$$=i^+j^+k^+$$λ(i^$$−$$j^$$−$$k^)  hence contains the point $$i^+j^+k^$$   and is normal to vector (i^+j^)(r$$→−$$(i^+j^+k^))⋅(i^+j^)=0or$$  $$x+y=2Plane$$ $$P2$$, contains the liner→$$=i^+j^+k^+$$λ$$(i^$$−$$j^$$−$$k^) and point $$j^Hence$$, equation of plane is x−$$0y$$−$$1z$$−$$01$$−$$01$$−$$11$$−$$01$$−$$1$$−$$1=0or$$  $$x+2y$$−$$z=2ff$$ θ is the acute angle between $$P1$$ and $$P2$$,then $$cos$$⁡θ$$=n1$$→⋅$$n2$$→|n→|$$n2$$→(i^+j^)⋅$$(i^+2j^$$−$$k^)2$$⋅$$6$$ $$=32$$⋅$$6=32$$θ$$=$$$$cos$$−$$1$$⁡$$32=$$π$$6$$  As L is contained in $$P2$$⇒θ$$=0$$

Let P1 denote the equation of a plane to which the vector (i^+j^) is normal and which contains the line whose equation r→=i^+j^+k^+λ(i^−j^−k^) and P2 denote the equation of the plane containing the line L and a point with position vector j^ Which of the following holds good?

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