if the lines `(vecr-(hati+hatj+hatk))X((1-p)hati+3hatj-2hatk)=0` and `(vecr-(3hati+hatj-5hatk))X((3-p)hati+4hatj-8hatk)=0` are coplaner then `p` is equal to

If the lines vecr-(hati+hatj+hatk) xx (1-p)hati+3hatj-2hatk=0 and (vecr-(3hati+hatj-5hatk)) xx (3-p)hati+4hatj-8hatk=0 are coplanar then the value of p is

If the lines hati-(hati+hatj+hatk) xx (1-p)hati+3hatj-2hatk=0 and (vecc-(3hati+hatj-5hatk)) xx (1-p)hati+3hatj-2hatk=0 are coplanar then the value of p is

The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and vecr=(hati+2hatj+3hatk)+mu(3hati+phatj+phatk) are perpendicular it p=

The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and vecr=(hati+2hatj+3hatk)+mu(3hati-phatj+phatk) are perpendicular it p=

The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and vecr=(hati+2hatj+3hatk)+mu(3hati-phatj+phatk) are perpendicular if p=

Find the shortest distance vecr=hati+2hatj+3hatk+lambda(hati-3hatj+2hatk)and vecr= 4hati+5hatj+6hatk+mu(2hati+3hatj+hatk) .

Shortest distance between the lines: vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+u(2hati+4hatj-5hatk)

Consider the lines vecr=hati+2hatj+3hatk+lambda(2hati+3hatj+4hatk) and vecr=2hati+3hatj+4hatk+mu(3hati+4hatj+5hatk) . i.Convert the equations to cartesian form ii. Show that the lines are not skew lines.

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