Question

L2 2 7 2. Find parametric and symmetric equations for the line through (2, 1,0) and perpendicular to both i +j and j+k. Dind +

Answer 1

Suppose the parametric equation for the line in equation is r = < 2m 1, 0 > + < a, b, c > then < a, b, c > . < 1, 1, 0 > = 0 Rightarrow a + b = 0 Rightarrow b = -a = -c < a, b, c > < 0, 1, 1 > = 0 Rightarrow b + c = 0 Rightarrow c = -b = a therefore a vector in the direction of the line is < 1, -1, 1 > so in parameter form the equation of the line is < x, y, z > = r < 2, 1, 0 > + t < 1,-1, 1 > i.e x = 2 + t y = 1 - t z = t this is parameter equation Now x = 2 + t Rightarrow t = x - 2 y = 1 - t Rightarrow t = 1 - y z = t Rightarrow t = z i.e t = x - 2 = 1 - y = z this is symmetric equation