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Vectors : Line Equations and Line Segments

1) Find the equation of the line passing through the point (6, 1, 8) in the direction of the vector (-3, 4, -2).
Write the equation in vector and coordinate form.
2) Find the equation of the line segment joining points (2, 4, 6) and (1, 7, 8), both in vector and coordinate
form. Be sure to specify the set of possible values of the parameter.
3) Given two vectors u = (2, 3, 1) and v = (4, 1, 0), represent v in the form v = r + w, where r is a scalar
multiple of u and w is orthogonal to u. (Write the components of r, w in simple fractions).

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Vectors, Line Equations and Line Segments are investigated. The solution is detailed and well presented.

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