Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0 . Question: What are the direction ratios of a line M parallel to the plane P ?

Step-by-step solution

The plane P is given by 2x + 3y + z + 5 = 0 . The direction ratios of the normal to the plane P are 2, 3, 1 . Since the line M is parallel to the plane P , its direction vector must be perpendicular to the normal vector of the plane. Let the direction ratios of the line M be a, b, c . Then, 2a + 3b + c = 0 . Checking the given options: For -3, 2, 1 , 2(-3) + 3(2) + 1 = 1 0 For 3, 2, -6 , 2(3) + 3(2) - 6 = 6 0 For 1, 3, 2 , 2(1) + 3(3) + 2 = 13 0 For 2, 2, -10 , 2(2) + 3(2) - 10 = 0 Thus, the direction ratios of the