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

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.

Show that the lines vecr=(6hati+hatj+2hatk)+s(hati+2hatj-3hatk) and vecr=(3hati+2hatj-2hatk)+t(2hati+4hatj-5hatk) are skew lines and hence find the shortest distance between them.

Show that the lines vecr=(-2hati-4hatj-6hatk)+t(hati+4hatj+7hatk) vecr=(hati+3hatj+5hatk)+s(3hati+5hatj+7hatk) are coplanar. Find the equation of such plane in non parametric form and in cartesian form.

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

Given the straight lines vecr=(3hati+2hatj-4hatk)+lambda(hati+2hatj+2hatk) and vecr=(5hatj-2hatk)+mu(3hati+2hatj+6hatk) i.Find the angle between the lines. ii. Obtain a unit vector perpendicular to both the lines. iii. Form the equation of the line perpendicular to the given lines and passing through the point (1,1,1).

Show that the lines vec r = hati + hatj + t(hati - hatj +3hatk) and vecr = 2hati + hatj -hatk + s(hati + 2hatj -hatk) intersect . Find the point of intersection.

Show that the lines vecr=(hati-hatj)+t(2hati+hatk) and vecr=(2hati-hatj)+s(hati+hatj-hatk) are skew lines and find the distance between them .

Statement 1 : Lines vecr= hati-hatj+ lamda (hati+hatj-hatk) and vecr= 2hati-hatj+ mu (hati+hatj-hatk) do not intersect. Statement 2 : Skew lines never intersect.