Prove that the normal to the planes `vec r. (2 hat i- hat j+3 hatk)=5 and vec r .(2 hat i-2 hatj-2 hatk)=5` are prepndicular to each other.

A unit vector parallel to the intersection of the planes vec r. \ ( hat i- hat j+ hat k)=5 \ a n d \ vec r. \ (2 hat i+ hat j-3 hat k)=4 a. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) b. (-2 hat i+5 hat j-3 hat k)/(sqrt(38)) c. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) d. (-2 hat i-5 hat j-3 hat k)/(sqrt(38))

A unit vector parallel to the intersection of planes vecr.( hati- hatj + hat k)=5 and vec r .(2 hati+ hatj-3 hatk)=4 is ___

Find the equation the plane which contain the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec r(5 hat i+3 hat j-6 hat k)+8=0 .

Show that the line of intersection of the planes vec r.( hat i+2 hat j+3 hat k)=0 and vec r.(3 hat i+2 hat j+ hat k)=0 is equally inclined to ia n dkdot Also find the angle it makes with jdot

If vec a= 2 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

if vec a = 2 hat i- 3 hat j+hat k and vec b = hat i+2 hat j- 3hat k then vec aXvec b is

Find the equation of a plane through the intersection of the planes vec(r). (hat(i) + 3hat(j) - hat(k)) =5 and vec(r). (2hat(i) - hat(j) + hat(k)) and passing through the point (2, 1, -2)

Find the equation of a plane through the intersection of the planes vecr.(hati+3hat j-hat k)=5 and vecr.(2hat i-hatj +hatk)=3 and passing through the point (2,1,-2)

Find | vec axx vec b| , if vec a= hat i-7 hat j+7 hat k and vec b=3 hat i-2 hat j+2 hat kdot

if vec a= 5 hat i -hat j -3 hat k and vec b=hat i+3 hat j - 5 hat k , Find vec a . vec b =?