If `vecr=(hati+2hatj+3hatk)+lambda(hati-hatj+hatk)` and `vecr=(hati+2hatj+3hatk)+mu(hati+hatj-hatk)` are two lines, then the equation of acute angle bisector of two lines is

If vecA= 5hati+6hatj+3hatk and vecB=6hati-2hatj-6hatk , then

Find the vector equation of the plane that contains the lines vec r=(hati+hatj)+lambda(hati+2hatj-hatk) and vec r=(hati+hatj)+mu(-hati+hatj-2hatk) .Also find the length of the perpendicular drawn from the point (2,1,4) to the plane thus obtained.

If veca=hati+3hatj+hatk, vecb=2hati-hatj-hatk and vec c=m hati+7hatj+3hatk are coplanar, then the value of m is -

Find whether the lines vec r=(hati-hatj-hatk)+lambda(2hati+hatj) and vecr=(2hati-hatj)+mu(hati+hatj-hatk) intersect or not. If intersecting find their point of intersection.

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

Find the vector and cartesion equations of a plane containing the two lines vec r=2hatj+hatj-3hatk+lambda(hati+2hatj+5hatk) and vec r=3hati+3hatj+2hatk+mu(3hati-2hatj+5hatk) .Also show that the line vec r=2hati+5hatj+2hatk+p(3hati-2hatj+5hatk) lies in the plane.

If the line vecr=(2hati-hatj+3hatk)+lambda(2hati+hatj+2hatk) is parallel to the plane vecr*(3hati-2hatj+p hatk)=4 then the value of p is -

Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7hati-hatk) are collinear.

The cosine of the angle between the lines vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr=5hati-2hatj+mu(3hati+2hatj+6hatk) is -

A vector perpendicular to both of (3hati+hatj+2hatk) and (2hati-2hatj+4hatk) is