The line L is passing through (1,2,3) . The distance of any point on the line L from the line r =(3 -1) i +(-2 +3) j +(4+ ) k is constant. Then the line L does not pass through the point

Step-by-step solution

Given line L' is parameterized as r = (- i + 3 j + 4 k ) + (3 i - 2 j + k ) . It passes through A(-1, 3, 4) with direction vector b = 3 i - 2 j + k . The distance from any point on line L to L' is constant, implying L is parallel to L' . Thus, L shares direction vector d = b and passes through P(1, 2, 3) , giving its parametric form as (1 + 3k, 2 - 2k, 3 + k) where k is a scalar. For a point to lie on L , the ratios x-1 3 = y-2 -2 = z-3 1 must be equal to some k . Points (4, 0, 4) , (-2, 4, 2) , and (7, -2, 5) sati