Final answer:
To find the parametric equations and symmetric equations for the line through (2, 2, 0) and perpendicular to both i j and j k, use the cross product of the two given vectors to find the direction vector of the line. Then, use the point-slope form of a line to find the parametric equations. Finally, eliminate the parameter to find the symmetric equations.
Step-by-step explanation:
To find the parametric equations and symmetric equations for the line through (2, 2, 0) and perpendicular to both i j and j k, we need to use the cross product of the two given vectors to find the direction vector of the line. The cross product of i j and j k is i k, so the direction vector is i k. Now we can use the point-slope form of a line to find the parametric equations: x = 2 + t, y = 2, and z = 0 + t. To find the symmetric equations, we can eliminate the parameter t: x - 2 = z - 0, or x - z = 2. Therefore, the parametric equations are x = 2 + t, y = 2, and z = t, and the symmetric equations are x - z = 2.