Show that the plane `vecr.(hati-3hatj+5hatk)=7` contains the line `vecr=(hati+3hatj+3hatk)+lambda(3hati+hatj)`

Prove that the plane vecr*(hati+2hatj-hatk)=3 contains the line vecr=hati+hatj+lamda(2hati+hatj+4hatk).

Find the angle between the following lines and the planes : (i) line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and planes vecr.(2hati-hatj+hatk) = 4 . (ii) line vecr = (2hati+3hatj+9hatk)+lambda(2hati+3hatj+4hatk) and plane vecr.(hati+hatj+hatk) =5 . (iii) line (x+1)/(3) = y/2 = z/4 and plane 2x+y-3z=5 . (iv) line (x-3)/(9) = (y+4)/(6) = (z+2)/(2) and plane 3x-y+z=0 .

Find the angle between the planes vecr.(3hati-4hatj+5hatk)=0 and vecr.(2hati-hatj-2hatk)=7 .

The ratio in which the plane vecr.(hati-2hatj+3hatk)=17 divides the line joining points -2hati+4hatj+7hatk and 3hati-5hatj+8hatk is

The angles between the planes vecr.(3hati-6hatj+2hatk)=4 and vecr.(2hati-hatj+2hatk)=3 , is

Show that the lines vecr=(2hatj-3hatk)+lambda(hati+2hatj+3hatk) and vecr = (2hati+6hatj+3hatk)+mu(2hati+3hatj+4hatk) are coplanar. Also the find the equation of the plane passing through these lines.

Find the vector and Cartesian forms of the equationi of the plane containing the two lines. vecr=(hati+2hatj-4hatk)+lambda(2hati+3hatj+6hatk) and vecr=(9hati+5hatj-hatk)+mu(-2hati+3hatj+8hatk) .

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 vector and Cartesian equations of a plane containing the two lines vecr=(2hati+hatj-3hatk)+lambda(hati+2hatj+5hatk) and vecr=(3hati+3hatj+2hatk)+mu(3hati-2hatj+5hatk) .