Show that the lines: vecr=(hati+hatj-hat...

Show that the lines: `vecr=(hati+hatj-hatk)+lambda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk)` are intersecting. Hence find their point of intersection.

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Show that the lines: vecr=(hati+hatj)+lambda(2hati-hatk) and vecr=(2hati-hatj)+mu(hati+hatk-hatk) do not intersect.

Check whether the lines vecr=hati+hatj-hatk+lambda(3hati-hatj) and vecr=4hati-hatk+mu(2hati+hatk) intersect or not.

Show that the lines : vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr=5hati-2hatj+mu(3hati+2hatj+6hatk) are intersecting. Hence, find their point of intersection.

Show that the lines vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk)and vecr=5hati-2hatj+mu(3hati+2hatj+6hatk) are intersecting. Also, find the point of intersection.

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

Show that the lines vecr=hati+hatj+hatk+lambda(hati-hatj+hatk) and vecr=4hatj+2hatk+mu(2hati-hatj+3hatk) are coplanar.

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

Find the equation of the line perpendicular to the lines : vecr=(3hati+2hatj-4hatk)+lambda(hati+2hatj-2hatk) and vecr=(5hatj-2hatk)+mu(3hati+2hatj+6hatk) and passing through the point (1,1,1)

Find the angle between the lines vecr=2hati+3hatj-4hatk+lambda(2hati+1hatj+2hatk) and vecr=2hati-5hatk+mu(6hati+3hatj+2hatk)

ACCURATE PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTIONS CARRYING 6 MARKS:

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