Question

Determine the point of the line

x+2y+z=1
2x+y+z=4

which is closest to the origin.

Answer 1

lol..this is the equation of plane and not line

Answer 2

the intersection gives line @Yahoo!

Answer 3

take the cross product to get the direction of line

Answer 4

\[\large \langle 1, 2, 1 \rangle \times \langle 2, 1, 1\rangle = \langle 1,1,-3\rangle \]

So, the plane perpendicular to the given line which passes through origin will be :
\(\large x+y-3z = 0 \)

Answer 5

the required point is the intersection of this plane and the given line