Show that the lines vec r = hati + hatj ...

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.

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Determine whether the lines vecr=(hati-hatj)+t(hati-hatj+3hatk) and vecr=(2hati+hatj-hatk)+s(hati+2hatj-hatk) are parallel. Find the shortest 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.

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.

Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-hatj+hatk) and vecr=(2hati+hatj-hatk)+s(2hati-hatj+hatk) .

Find the angle between the lines vecr=hati-hatj+hatk+lambda(2hati-2hatj+hatk) and vecr=2hati-hatj+2hatk+mu(hati+hatj+2hatk) .

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 .

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.

Show that the lines vecr=(3hati+5hatj+7hatk)+t(hati-2hatj+hatk) vecr=(hati+hatj+hatk)+s(7hati+6hatj+7hatk) are skew lines and find the shortest distance between them.

Show that the vectors hati+2hatj-3hatk , 2hati-hatj+2hatk and 3hati+hatj-hatk are coplanar.

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