Final answer:
To find a perpendicular line to a 3D parametric equation, identify the directional vector of the original line and use the cross product with a non-parallel vector to determine a new vector that is perpendicular to the first.
Step-by-step explanation:
To find a perpendicular line to a given 3D parametric equation, we need to understand some key concepts of vector mathematics. First, we identify the directional vector of the original line. We can then utilize this directional vector to find one that is perpendicular. In 3D, a line can be expressed in parametric form as x = x_0 + at, y = y_0 + bt, and z = z_0 + ct, where (x_0, y_0, z_0) is a point on the line, and (a, b, c) is the directional vector.
For adding vectors using perpendicular components, one can analyze the resulting vector R which is the sum of vectors A and B. The components of a vector, say A, along the x- and y-axis are calculated using Ax = A cos θ and Ay = A sin θ.
Next, to find a 3D line perpendicular to the original, we use the cross product. If vector A represents the direction of the line, then any vector that is perpendicular to A can serve as a direction vector for the perpendicular line. We can use a standard basis vector (such as i, j, or k) or another vector not parallel to A, say B, and calculate the cross product A × B. This cross product will give us a new vector C that is perpendicular to both A and B.
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