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Unformatted text preview: Math 23 B. Dodson Week 2 Homework: 12.5 Lines, Planes 12.6 Quadratic Surfaces Problem 12.5.3: Give vector and (scalar) parametric equations for the line through the point (-2,4,10) parallel to the vector < 3 , 1 , 8 > . Solution: The vector equation vector OP = vector OP + t vector d, for when the position vector of the point P ( x, y, z ) puts P on the line through P ( x , y , z ) with direction vector vector d = < a, b, c > gives < x, y, z > = < x , y , z > + t < a, b, c > = <- 2 , 4 , 10 > + t < 3 , 1 , 8 >, which we can view as a point-slope equation, where P is the point, and vector d gives the direction of the line. (Here in the position vector vector OP, O = O (0 , , 0) is the Origin.) To get the scalar equations, we use scalar mult. and vector add to write the vector equation 2 . as < x, y, z > = <- 2 + 3 t, 4 + t, 10 + 8 t >, and simply read-off x =- 2 + 3 t, y = 4 + t, z = 10 + 8 t....
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