Question

Find a vector equation with parameter t for the line of intersection of the planes x y z=2 and x z=0.

Answer 1

The vector equation for the line of intersection of the planes x+y+z=2 and x+z=0 is r(t) = -ti + 2j - tj.

Step-by-step explanation:

To find a vector equation for the line of intersection of the planes x+y+z=2 and x+z=0, we can solve these two equations simultaneously. From the second equation, we have x = -z. Substituting this into the first equation, we get -z+y+z=2, which simplifies to y=2. Therefore, the line of intersection is given by the parameterized equation r(t) = -ti + 2j - tj, where t is a real number.