Prove that the volume of tetrahedron bounded by the planes
`vecr.(mhatj+nhatk)=0,vecr.(nhatk+lhati)=0,vecr.(lhati+mhatj)=0, vecr.(lhati+mhatj+nhatk)=P" is"(2p^(3))/(3lmn)`

The plane through the point (-1,-1,-1) nd containing the line of intersection of the planes vecr.(hati+3hatj-hatk)=0 ,vecr.(hatj+2hatk)=0 is (A) vecr.(hati+2hatj-3hatk)=0 (B) vecr.(hati+4hatj+hatk)=0 (C) vecr.(hati+5hatj-5hatk)=0 (D) vecr.(hati+hatj-3hatk)=0

Find the line of intersection of the planes vecr.(3hati-hatj+hatk)=1 and vecr.(hati+4hatj-2hatk)=2

The angle between the planes vecr. (2 hati - 3 hatj + hatk) =1 and vecr. (hati - hatj) =4 is

Let A bet eh given point whose position vector relative to an origin O be veca and vec(ON)=vecn. let vecr be the position vector of any point P which lies on the plane passing through A and perpendicular to ON.Then for any point P on the plane, vec(AP).vecn=0 or, (vecr-veca).vecn=0 or vecr.vecn=veca.vecn or , vecr.hatn=p where p ils the perpendicular distance of the plane from origin. The equation of the plane through the point hati+2hatj-hatk and perpendicular to the line of intersection of the planes vecr.(3hati-hatj+hatk)=1 and vecr.(-hati-4hatj+2hatk)=2 is (A) vecr.(2hati+7hatj-13hatk)=29 (B) vecr.(2hati-7hatj-13hatk)=1 (C) vecr.(2hati-7hatj-13hatk)+25=0 (D) vecr.(2hati+7hatj+13hatk)=3

The vector equation of the line of intersection of the planes vecr.(2hati+3hatk)=0 and vecr.(3hati+2hatj+hatk)=0 is

Find the angle between the planes vecr.(hati+hatj-2hatk)=3 and vecr.(2hati-2hatj+hatk)=2 2

The angle between hati and line of the intersection of the plane vecr.(hati+2hatj+3hatk)=0andvecr.(3hati+3hatj+hatk)=0 is

Find the equation of the plane through the line of intersection of the planes vecr.(2hati-3hatj+4hatk)=1 and vecr.(hati-hatj)+4=0 and perpendicular to the plane vecr.(2hati-hatj+hatk)+8=0 .

Let A be the given point whose position vector relative to an origin O be veca and vec(ON)=vecn. let vecr be the position vector of any point P which lies on the plane passing through A and perpendicular to ON.Then for any point P on the plane, vec(AP).vecn=0 or, (vecr-veca).vecn=0 or vecr.vecn=veca.vecn or , vecr.hatn=p where p ils the perpendicular distance of the plane from origin. The equation fo the plane which ponts contains the line vecr=2hati+t(hatj-hatk0 where it is scalar and perpendicular to the plane vecr.(hati-hatk)=3 is (A) vecr.(hati-hatj-hatk)=2 (B) vecr.(hati+hatj-hatk)=2 (C) vecr.(hati+hatj+hatk)=2 (D) vecr.(2hati+hatj-hatk)=4

Prove that the plane vecr*(hati+2hatj-hatk)=3 contains the line vecr=hati+hatj+lamda(2hati+hatj+4hatk).