`lambda ` के किस मान के लिए समतल ` vecr .( 2hati +lambda hatj -3hatk )=2` तथा ` vecr .(lambda hati - 3hatj +hatk ) =5` एक दूसरे पर लम्ब होंगें|

Find the angle between the line vecr = (hati +2hatj -hatk ) +lambda (hati - hatj +hatk) and vecr cdot (2hati - hatj +hatk) = 4.

Find the angle between the line vecr.(3hati+hatk)+lambda(hatj+hatk) and the plane vecr.(2hati-hatj+2hatk)=1 .

Show that the line vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr.(hati+2hatj-hatk)=3

The angle between the line vecr=( hati+2 hatj- hatk)+ lambda( hati- hatj+ hatk) and the plane vecr. (2 hati- hatj+ hatk)=4 is __

The distance between the line vecr = 2hati - 2hatj + 3hatk + lambda (hati-hatj + 4hatk) and the plane vecr. (hati + 5hatj + hatk) = 5 is

The shortest distance between the lines vecr = (2hati - hatj) + lambda(2hati + hatj - 3hatk) vecr = (hati - hatj + 2hatk) + lambda(2hati + hatj - 5hatk)

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .