Direction: Consider the following for the items that follow:

Let S be the line of intersection of two planes x + y + z = 1 and 2x + 3y - 4z = 8.  

If 〈l, m, n〉 are direction cosines of S, then what is the value. of 43 (I² - m² - n²)?  

Direction: Consider the following for the items that follow:

Let L : x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P : x + 2y + 3z + 1 = 0 be a plane. 

What are the direction ratios of the line?  

Direction: Consider the following for the items that follow:

Let L : x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P : x + 2y + 3z + 1 = 0 be a plane. 

What is the point of intersection of L and P? 

Let z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?