Determine the vector equation of a plane that contains the line with symmetric x+3 equation *+-+12+2 and the point P(1,3,0). 5 7- (1,3,0) + s(-2,5,4) + t(3, 1, 2), s,t € R OF(1,3,0) + s(-2,5,4) + (4,4,2), s,£ € R OF(1,3,0) + 5 (-2,5,4) + (1,3,0), s,£ € R none of the above

What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z = 12? 3x - 7z+9 = 0 3x - 7z+ 12 = 0 3x - 7z - 35= 0 O 3x - 7z +52 = 0

Let Ly be the line passing through the point P-(10, 1, -10) with direction vector d-[-2, -2, 3]", and let L2 be the line passing through the point P-(-10, 21, -6) with direction vector d,-[-2, -6, -1]". Find the shortest distance d between these two lines, and find a point Q, on L, and a point Q, on L2 so that d(Q7 Q2) = d. Use the square root symbol W where needed to give an exact value for your answer. d = 0 Qi = 1%3D(0,0,0) Q2 = (0, 0, 0)

Which vector equation below represents the line in R³ that passes through the point (-4, 5, 7) and is perpendicular to both a = and b = ? - Or(t) = 4, 5, 7> OF(t) = Or(t) = 4, 5, 7> + t 1 + t Or(t)= 4, 5, 7> + t Or(t) =