Answer Save. 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? – 3, – 5, – 3 The direction ratios of PR are 5 – 2, 8 – 3, 7 –4 i.e. Steve4Physics. 3, 5, 3 Since ∴ lines PQ and PR are parallel. (ii) By equating i, j and k components on both sides, the vector equation of the straight line passing through P Why are the direction ratios of parallel lines 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 Relevance. 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. ... Lines are parallel if the direction vectors are in the same ratio. 1 Answer. n = cos 0 = 1. 11.1.8 If l 1, m 1, n 1 and l 2, m 2, n 2 are the direction cosines of two lines … 11.1.4 Direction ratios of a line are the numbers which are proportional to the direction cosines of the line. 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. The direction ratios of PQ are –1, –2, –2 –3, 1 – 4 i.e. Therefore, direction cosines of a line parallel to the z − axis are 0, 0, 1. But P is a common point on both the lines points ∴ P, Q, R are collinear. 3, 5, 3 Since ∴ lines PQ and PR are parallel. Thus, the direction cosines are given by. 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 But P is a common point on both the lines points ∴ P, Q, R are collinear. l = cos 90 ° = 0 m = cos 90 ° = 0 . 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. – 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. We know that, Two lines with direction ratios a 1 , b 1 , c 1 and a 2 , b 2 , c 2 are perpendicular to … The components of a form a set of direction ratios for the straight line. The direction ratios of PQ are –1, –2, –2 –3, 1 – 4 i.e. do parallel vectors lines have same direction ratios - Mathematics - TopperLearning.com | 4q0xuqnn 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. Lv 7.