Find the vector equation of the followin...

Find the vector equation of the following plane in scalar product form: `vecr=hati-hatj+lambda(hati+hatj+hatk)+mu(hati-2hatj+3hatk)`

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Find the vector equation of the following planes in scalar product form: vecr=2hati-hatk+lambdahati+mu(hati-2hatj-hatk) .

Find the vector equation in scalar product form of the plane vecr=2hati-hatj+lambda(hati+2hatj+3hatk)+mu(2hati-hatj-3hatk) .

Find the angles between each of the following pairs of lines: vecr=4hati-hatj+lambda(hati+2hatj-hatk) and vecr=hati-hatj+2hatk-mu(2hati+4hatj-4hatk)

Find the equation of the plane containingg the lines: vecr=hati+hatj+lambda(hati+2hatj-hatk) and vecr=hati+hatj+mu(-hati+hatj-2hatk) . Find the distance of this plane from origin and also from the point (1,1,1).

Determine whether or not the following paris of lines intersect: vecr=hati-hatj+lambda(2hati+hatk) , vecr=2hati-hatj+mu(hati-hatj-hatk)

Determine whether or not the following pairs of lines intersect : vecr=(hati-2hatj+3hatk)+lambda(-hati+hatj-2hatk) and vecr=(hati-hatj-hatk)+mu(hati+2hatj-2hatk)

Determine whether or not the following paris of lines intersect: vecr=hati-5hatj+lambda(2hati+hatk) , vecr=2hati-hatj+mu(hati+hatj-hatk) .

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 following pair of lines: vecr = 3hati+hatj-2hatk + lambda(hati-hatj-2hatk) and vecr = 2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the shortest distance between each of the following pair of lines: vecr=(4hati-5hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) .

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE

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