The image of the point `(1, 2, 3)` about the line `vecr = (2hati+ 3hatj-hatk) + lambda(hati – 2hatj + 2hatk)` is

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 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 image of the point (3hati-hatj+11hatk) in the line vecr = 2 hatj + 3hatk+lambda(2hati+3hatj+4hatk) .

Find the image of the point (3hati-hatj+11hatk) in the line vecr = 2 hatj + 3hatk+lambda(2hati+3hatj+4hatk) .

Find the points of intersection of the line vecr = (2hati - hatj + 2hatk) + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

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 plane passing through the point (1,1,1) and containing the line: vecr=(-3hati+hatj+5hatk)+lambda (3hati-hatj+5hatk) . Also, show that the plane contains the line: vecr=(-hati+2hatj+5hatk)+lambda(hati-2hatj-5hatk) .

Find the points of intersection of the line vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk) and the plane vecr.(hati - hatj + hatk) = 5

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) .