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Find the vector and cartesian equations of the line through the point `(1, 2, - 4)` and perpendicular to the two lines- `vecr=(8hati - 19 hatj + 10hatk) + lambda(3hati - 16hatj + 7hatk)` and `vecr=(15hati + 29hatj + 5hatk) + mu(3hati +8hatj - 5hatk).`

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Find the vectoer and cartesian equations of the line through the point (1,2,-4) and perpendicualr of the lines: vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) and vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-5hatk)

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

Find the vector and Cartesian equations of the plane passing through the point (1,2,-4) and parallel to the lines vecr=(hati+2hatj+hatk)-lambda(2hati+3hatj+6hatk) and vecr=(hati-3hatj+5hatk)+mu(hati+hatj-hatk) .

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

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

Find the equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

Find the vector and Cartesian quations of the plane passing through the point (3,-1,2) and parallel to the lines vecr=(-hatj+3hatk)+lambda(2hati-5hatj-hatk) and vecr.(hati-3hatj+hatk)+mu(-5hati+4hatj) .

The shortest distance between the lines vecr = (2hati - hatj) + lambda(2hati + hatj - 3hatk) vecr = (hati - hatj + 2hatk) + lambda(2hati + hatj - 5hatk)