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3 cards from this section. Quick, good the night before a test.
Write the parametric equations for a line that passes through (2, 3, 4) with direction ratios (1, 2, 3).
Use the point and direction ratios to construct the equations.
If λ = 2 for the previous equations, what are the coordinates?
Substitute λ into your parametric equations.
What is the meaning of the parameter λ in parametric equations?
Think about how λ controls the points on the line.
True or False: The parametric equations for a line in space can be used to find the coordinates of any point on the line.
Recall how changing λ affects point locations.
Find the parametric equations of a line if it passes through (2, 3, 4) and is parallel to the vector (1, 2, 1).
Start with the point coordinates and add the direction ratios scaled by λ.
Two lines are parametrically defined as L₁: (x, y, z) = (1 + t, 2 + 2t, 3 + 3t) and L₂: (x, y, z) = (4 - s, 5 - 2s, 6 + s). Determine if these lines intersect.
Formulate a system of equations and check for solutions.
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