Question

Consider the points P(2, 1, 1) and Q(3, 0, 0).

(a) Write the equation of the line that passes through the points P and Q. Express your answer with both parametric equations and symmetric equations.

(b) Write the equation of the plane (in terms of x, y, z) that passes through the point P and is perpendicular to the line from part (a).

Answer 1

som substracting the position vectors of the two points gives the digestion vector, which is - J = på? = <1, , 1) we can either sef p or & as (249/192). using p would give - 1-2 ='-19+) = -(24) and in parametric form, it would be - - 2 = y 2 = 2 2 2 = => a=t+2 a Y=ottl, 2=-tt And Now, the plane is perpendicular to the line Des Therefore the normal of the plane is direction cosine of the line. So, the equation of plene conturining the point P (2,191) is - 9L0-N) + b17-7)+c (2-2) 20 => 1.(M-2) +6+1)(y-1)+ 61(2-1)=0 5) -2-4+1 --Z+1=0 => n-y-z=0 Ang