11.1.4 Direction ratios of a line are the numbers which are proportional to the direction cosines of the line. The components of a form a set of direction ratios for the straight line. – 3, – 5, – 3 The direction ratios of PR are 5 – 2, 8 – 3, 7 –4 i.e. Notes: (i) The vector equation of a straight line passing through the origin and parallel to a given vector a will be of the form r = ta. Parallel Lines and Proportionality In the Triangle Proportionality Theorem , we have seen that parallel lines cut the sides of a triangle into proportional parts. A line parallel to z − axis, makes an angle of 90 °, 90 ° and 0 ° with the x, y and z axes, respectively. Thus, the direction cosines are given by. 3, 5, 3 Since ∴ lines PQ and PR are parallel. do parallel vectors lines have same direction ratios - Mathematics - TopperLearning.com | 4q0xuqnn l = cos 90 ° = 0 m = cos 90 ° = 0 . But P is a common point on both the lines points ∴ P, Q, R are collinear. n = cos 0 = 1. – 3, – 5, – 3 The direction ratios of PR are 5 – 2, 8 – 3, 7 –4 i.e. Why are the direction ratios of parallel lines same? We know that, Two lines with direction ratios a 1 , b 1 , c 1 and a 2 , b 2 , c 2 are perpendicular to … But P is a common point on both the lines points ∴ P, Q, R are collinear. 11.1.5 If l, m, n are the direction cosines and a, b, c are the direction ratios of a line, ... parallel to each of the skew lines. Therefore, direction cosines of a line parallel to the z − axis are 0, 0, 1. The direction ratios of PQ are –1, –2, –2 –3, 1 – 4 i.e. I got an example in my textbook showing that if Direction Ratios(DR) of a line are a,b,c then a line parallel will have DR ka,kb,kc which is a,b,c.If the lines are parallel how can DR be same? Direction Cosines and Direction Ratios of a Line video tutorial 00:33:19; Direction Cosines and Direction Ratios of a Line video tutorial 00:31:29; Direction Cosines and Direction Ratios of a Line video tutorial 00:41:23 ... Lines are parallel if the direction vectors are in the same ratio. Note 2 : The condition for the lines to be parallel is 1 11 2 22 lm n lm n == THEOREM If (a1, b1, c1) and (a2, b2, c2) are direction ratios of two lines and θ is the angle 11.1.8 If l 1, m 1, n 1 and l 2, m 2, n 2 are the direction cosines of two lines … Answer Save. Relevance. Steve4Physics. Lv 7. (ii) By equating i, j and k components on both sides, the vector equation of the straight line passing through P Lessons on Vectors: Parallel Vectors, how to prove vectors are parallel and collinear, conditions for two lines to be parallel given their vector equations, Vector equations, vector math, with video lessons, examples and step-by-step solutions. 3, 5, 3 Since ∴ lines PQ and PR are parallel. The direction ratios of PQ are –1, –2, –2 –3, 1 – 4 i.e. Similarly, three or more parallel lines also separate transversals into proportional parts. The direction ratios of the given lines are 7, -5, 1 and 1, 2, 3, respectively. 1 Answer.