Find the vector and Cartesian quations o...

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)`.

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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) .

The equation of line passing through (3,-1,2) and perpendicular to the lines vecr=(hati+hatj-hatk)+lamda(2hati-2hatj+hatk) and vecr=(2hati+hatj-3hatk) +mu(hati-2hatj+2hatk) is

Find the vector equation of the plane passing through the point (3hati+4hatj+2hatk) and parallel to the vectors (hati+2hatj+3hatk) and (hati-hatj+hatk) .

Find the vector equation of the plane through the point (3hati+4hatj-hatk) and parallel to the plane vecr(2hati-3hatj+5hatk)+5=0 .

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr*(hati-hatj+2hatk)=5 and vecr*(3hati+hatj+hatk)=6 .

Find the vector equation of the plane passing through the point (1,1,1) and passing through the intersection of the planes vecr.(hati-hatj+3hatk)+1=0 and vecr.(2hati+hatj-hatk)-5=0 .

Find the vector equation o the line passing through (1,2,3) and parallel to the planes vecr.(hati+hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6

Find the shortest distance the lines vecr = hati+hatj+lambda(2hati-hatj+hatk) and vecr = (2 hati+hatj+hatk) - mu (3hati-5hatj)

Find the angle between the lines vecr = (hati+hatj)+lambda (hati+hatj+hatk)and vecr=(2hati-hatj)+t(2hati+3hatj+hatk)

RS AGGARWAL-THE PLANE-Exercise 28G

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