1 Plot and label the following two lines on engineering paper, with 1 unit = 1cm (2 pts)
Line A 0x + 1y = 2
Line B 1x + 1y = 3
2 Find and label coordinates of the point where the lines intersect. (2 pts)
Note that the point of intersection is the same as where the following three planes intersect:
Plane A 0x + 1y + 0z = 2
Plane B 1x + 1y + 0z = 3
Plane C 0x + 0y + 1z = 0
x = 1 y = 2
.
4 Draw and label a normal from the origin to each line. The normal to line A is “a” and the
normal to line B is “b”. Put an arrowhead on each normal where it touches the line. (2 pts)
5 Measure the distance from the origin to each line (include 3 significant figures in your
answer). The distance is positive if the normal points from the origin to the line. For a
refresher on significant figures, see
(2 pts)
Distance from origin to line A (dA) 2.000
Distance from origin to line B (dB) 2.121
6 Label and measure the angles between the normal to each line and the x- and y-axes (this is a
total of four angles). For example, the angle between “a” and the x-axis is θax. (4 pts)
θax 90° θay 0°
θbx 45° θby 45°
7 Find the cosines of the angles between each line and the x- and y-axes (this is a total of four
cosines). For example, the cosine of θax is nAx. (4 pts)
nAx 0 nAy 1
nBx 0.7071 nBy 0.7071
8 Write the equation of each line in the form below, filling in the values for the cosine terms.
nAx x + nAy y = dA 0x + 1y = 2
nBx x + nBy y = dB 0.7071x + 0.7071y = 2.12 (2 pts)
9 Using your answer for (2) and eqs. (8), solve for dA (2.000) and dB (2.121) (2 pts)
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