One line passes through the points (-7,5) and (-1,-3). Another line passes through points (0,3) and (3,-1). Are the lines parallel, perpendicular, or neither?

Determine whether each statement is true or false in.

(a) Two lines parallel to a third line are parallel.

(b) Two lines perpendicular to a third line are parallel.

(c) Two planes parallel to a third plane are parallel.

(d) Two planes perpendicular to a third plane are parallel.

(e)Two lines parallel to a plane are parallel.

(f) Two lines perpendicular to a plane are parallel.

(g) Two planes parallel to a line are parallel.

(h) Two planes perpendicular to a line are parallel.

(i) Two planes either intersect or are parallel.

(j) Two lines either intersect or are parallel.

(k) A plane and a line either intersect or are parallel.

In this exercise, we find a formula for the angle formed by two lines in a coordinate plane. 

(a) If is a line in the plane and is the angle formed by the line and the -axis as shown in the figure, show that the slope of the line is given by 

(b) Let and be two nonparallel lines in the plane with slopes and , respectively. Let be the acute angle formed by the two lines (see the following figure). Show that 

(c) Find the acute angle formed by the two lines

and  

(d) Show that if two lines are perpendicular, then the slope of one is the negative reciprocal of the slope of the other. [Hint: First find an expression for .]