Case 6. Line inclined to HP and VP
When a line is inclined to both HP and VP,  the  apparent  inclination of the line to both the projection planes will be different from the actual inclinations. Similarly the projected length of the lines on to the planes will not be the same as the true length f the line. The following notation will be used for the inclinations and length of the lines for this entire lecture series:
 
Actual inclinations are θ degrees to HP  and  φ degrees to VP.
Apparent Inclinations are a and b to HP and VP respectively.
The Apparent Lengths of line AB are ab and a΄b΄in the top view and front view respectively.

Example:  Draw the projections of a line AB inclined to both HP and VP, whose true length and true inclinations and locations of one of the end points, say A are given.

The projections of the line AB are illustrated in figure 1. Since the line AB is inclined at θ to HP and φ to VP – its top view ab and the front view a΄b΄ are not in true lengths and they are also not inclined at angles θ to HP and φ to VP in the Front view and top view respectively. Figure 2 illustrates the projections of the line AB when the line is rotated  about A and made parallel to VP and HP respectively. A clear understanding of these can be understood if the procedure followed in the subsequent sub-sections are followed:

 

Figure 1:  The projections of a line inclined to both HP and VP