Question

Show that the lines 41 and 42 with parametric equations below are skew lines; that is, they do not intersect and are not parallel (and therefore do not lie in the same plane). X = 1 + 4t y = -2 + 12tZ = 4 - 4t x = 25 y - 3+ 5 z = -3 + 45

Answer 1

To show that the lines 41 and 42 are skew lines, we compare their direction vectors and demonstrate that they are not parallel or intersecting.

Step-by-step explanation:

To show that the lines 41 and 42 are skew lines, we need to demonstrate that they are neither parallel nor intersecting. We can do this by comparing the direction vectors of the two lines. For line 41, the direction vector is (4, 12, -4). For line 42, the direction vector is (5, 5, 45). Since the direction vectors are not scalar multiples of each other, the lines are not parallel. To determine if they intersect, we can set the parametric equations equal to each other and solve for t. However, their equations never yield the same value of t, indicating that they do not intersect. Therefore, the lines are skew lines.

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