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3 cards from this section. Quick, good the night before a test.
Write the symmetric form for the line passing through (1, 2, 3) with direction ratios (4, 5, 6).
Use the structure \\( \\frac{x - x_1}{a} = \\frac{y - y_1}{b} = \\frac{z - z_1}{c} \\).
What are the direction ratios of the line given by the symmetric form: (x-1)/3 = (y-4)/2 = (z-5)/1?
Identify the numbers in the denominator of the ratios.
What is the Symmetric Form of a line in 3D?
Think about what ratios represent in relations to lines.
True or False: The Symmetric Form can be used to determine if two lines are parallel.
What do direction ratios tell us about lines?
Identify if the following lines represented by their symmetric forms intersect: A: (x-1)/2 = (y+3)/3 = (z-4)/1 and B: (x+2)/2 = (y-5)/-1 = (z+1)/0.
Align the equations correctly.
Determine the angle between two lines expressed in symmetric forms: A: (x-1)/1 = (y-2)/2 = (z-3)/-3 and B: (x+3)/3 = (y-1)/1 = (z+2)/1.
Remember the angle can be determined using cosines via direction ratios.
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