The vector equation of the plane through the point `2hati-hatj-4hatk` and parallel to the plane `vecr.(4hati-12hatj-3hatk)-7=0`, is

Find the vector equation of the plane through the point (3hati+4hatj-hatk) and parallel to the plane vecr(2hati-3hatj+5hatk)+5=0 .

(i) Find the equations of the plane passing through (a,b,c) and parallel to the plane vec(r) . (hati + hatj + hatk) = 2 . (ii) Find the vector equation of the plane through the point hati + hatj + hatk and parallel to the plane vec(r). (2 hati - hatj + 2 hatk) = 5 .

The equation of plane passing through the point hati+hatj+hatk and paralel to the plane vecr.(2hati-hatj+2hatk)=5 is

Find the vector equation of the plane passing through the point (3hati+4hatj+2hatk) and parallel to the vectors (hati+2hatj+3hatk) and (hati-hatj+hatk) .

Find the equation of the plane through the point (3,4,-1) and parallel to the plane vecr.(2hati-3hatj+5hatk)+7=0

Find the vector equation to the plane through the point -hati+3hatj+2hatk perpendicular to each of the planes vecr.(hati+2hatj+2hatk)=25 and vecr.(3hati+3hatj+2hatk)=8.

Find the vector and Cartesian equations of the plane passing through the point (1,2,-4) and parallel to the lines vecr=(hati+2hatj+hatk)-lambda(2hati+3hatj+6hatk) and vecr=(hati-3hatj+5hatk)+mu(hati+hatj-hatk) .

Find the distance of the point (2hati-hatj-4hatk) from the plane vecr.(3hati-4hatj+12hatk)=9 .

The vector equation of a line passing through the point hati + 2hatj + 3hatk and perpendicular to the vectors hati +hatj + hatk and 2hati - hatj + hatk is