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 (-1,-5,-10) from the point of the intersection of the line vecr = 2hati-2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk) = 5 .

Find the distance of the pont (-1,-5,-10) from the point of intersection of the ine vecr.=2hati-hatj2hatklamda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk)=5 .

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 :

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 vecr=(2hati-hatj+3hatk)+lambda(3hati-hatj+2hatk) and the plane vecr.(hati+hatj+hatk)=3 .

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

Angle between the line vecr=(2hati-hatj+hatk)+lamda(-hati+hatj+hatk) and the plane vecr.(3hati+2hatj-hatk)=4 is

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

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