The line passing through the point (5,1, a) and (3, b, 1) crosses the yz-plane at (0, 17 2 , -13 2 ) , then the value of 2 a+3 ~b is

Step-by-step solution

The line through P₁ = (5, 1, a) and P₂ = (3, b, 1) has direction ratios determined by their coordinates. The symmetric form of its equation is: x - 5 3 - 5 = y - 1 b - 1 = z - a 1 - a = which simplifies to: x - 5 -2 = y - 1 b - 1 = z - a 1 - a = This line intersects the yz-plane where x = 0 . Substituting gives: 0 - 5 -2 = so = 5 2 . Using the known intersection point (0, 17 2 , -13 2 ) and = 5 2 , solve for b from the y-component: 17 2 - 1 b - 1 = 5 2 15 2 b - 1 = 5 2 15 b - 1 = 5 b - 1 = 3 b = 4 Similarly, from t