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Show that the lines (x - 1)/4 = (2 - y)/6 = (z - 4)/12 and (x - 3)/-2 = (y - 3)/3 = (5 - z)/6 are parallel. |
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Answer» We observe that the straight line (x - 1)/4 = (2 - y)/6 = (z - 4)/12 is parallel to the vector 4\(\hat {i}\) - 6\(\hat {j}\) + 12\(\hat {k}\) and the straight line (x- 3)/-2 = (y - 3)/3 = (5 - z)/6 is parallel to the vector. -2\(\hat {i}\) + 3\(\hat {j}\) - 6\(\hat {k}\). Since 4\(\hat {i}\) - 6\(\hat {j}\) + 12\(\hat {k}\), = -2(-2\(\hat {i}\) + 3\(\hat {j}\) - 6\(\hat {k}\)) the two vectors are parallel, and hence the two straight lines are parallel. |
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