The angle between the line `vecr = ( 5 hati - hatj - 4 hatk ) + lamda ( 2 hati - hatj + hatk) and ` the plane `vec r.( 3 hati - 4 hatj - hatk) + 5=0` is

The acute angle between the line bar r = ( hati + 2 hatj + hatk ) + lamda (hati + hatj +hatk) and the plane bar r ( 2hati - hatj +hatk)=5

(i) Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk) and the plane vec(r).(hati - hatj + hatk) = 5. (ii) Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - hatj + hatk)= 5. (iii) Find the distance of the point (2,12, 5) from the point of intersection of the line . vec(r) = 2 hati - 4 hatj + 2 hatk + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - 2 hatj + hatk ) = 0.

The shortest distance between the lines r = ( - hati - hatj - hatk ) + lamda ( 7 hati - 6 hatj + hatk ) and r = ( 3 hati + 5 hatj + 7 hatk ) + mu ( hati - 2 hatj + hatk )

If the point of intersection of the line vecr = (hati + 2 hatj + 3 hatk ) + ( 2 hati + hatj+ 2hatk ) and the plane vecr (2 hati - 6 hatj + 3 hatk) + 5=0 lies on the plane vec r ( hati + 75 hatj + 60 hatk) -alpha =0, then 19 alpha + 17 is equal to :

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

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

Find the angle between the line barr = (hati + 2hatj + hatk) + lambda(hati +hatj + hatk) and the plane barr*(2hati - hatj + hatk) = 5 .

Find the angle between the line vecr = (2hati+hatj-hatk)+lambda(2hati+2hatj+hatk) and the plane vecr.(6hati-3hatj+2hatk)+1=0 .

Find the points of intersection of the line vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk) + lambda ( 3 hati + 4 hatj + 12 hatk) with the plane vec(r). (hati - hatj + hatk) = 5 .