(18) Find the ratio in which the join of the points A(12, –5) andB(3, 4) is cut by the line r (3i – 11j) = 0. Show that the linejoining the origin to the point dividing AB externally in thesame ratio is perpendicular to the line r - (3i – 11j) = 0.(19) Find the equations of the sides of the square which has the point(-1, 1) as one vertex and the line r (3i + j) – 3 = 0 for onediagonal.(20) The points A(3, –1), B(-2, 4), C(-1,7) are three vertices ofthe quadrilateral ABCD. Given that the triangle ADC is thereflection in the line AC of triangle ABC, find the positionvector of D.(21) Find the reflection of the point (2, 1) in the line with equationr: (5i – j) + 3 = 0. Hence find the reflection in L of the liner:(i - j) –1 = 0.(22) Find the mirror images of the point B(3, 4) and the line3i + 4j + t(13i + j) in the line r (3i +7j) +2 = 0. (1) Find the perpendicular distances of(a) the point (-6, 2) from the line r (5i+ 12j) = 7;(b) the point (3, 4) from the line r - (3i + 4j) = 10;(e) the point (2, -3) from the line r (i – 5j) – 1 = 0;(d) the origin from the line r - (7ị – 3j) – 29 = 0.(2) Find the position vector of of the foot of the perpendicular fromthe point with position vector đị – 2j to the line r-(2i – 3) = 1.(3) Find the length of the altitude of the triangle A(2, 1), B(–1,3), C(-4, –3)from B to AC.(4) If Q is the foot of the perpendicular from (8,7) to the linejoining A(3, 6) to B(9, 2), find the position vector of Q, and theratio in which Q divides AB.(5) P and Q are the feet of the perpendiculars from A(0, 5) andB(-6,0) to the line r:(-i+2;) = 4. Find(a) the equations of AP and BQ.the distance PQ,(c) the position vector of the point of intersection of AQ withthe r-axis.(6) Find the distances between the following pairs of parallel lines:(a) r - (i + j) + 7 = 0, r · (i +¿) – 11 = 0;(b) r- (2i – 3) + 6 = 0, r · (di – 6) +5 = 0;(c) r • (4i – 3) – 9 = 0, r · (di – 3) – 24 = 0;(d) r = i+j+s(4i –i). r = 4ị + 5j +t(8į – 25)(7) Find the equations of the bisectors of the angles between thefollowing pairs of lines and, in each case, discriminate betweenthem:(a) r- (2i + j) + 4 = 0, r · (2i – 4j) – 7 = 0;(b) r- (3i + 4j) + 5 = 0, r - (5i + 12j) + 13 = 0;(d) r- (3i + 4) – 12 = 0, r - (3i – j) – 5 = 0;(e) r- (24i +7j) = 20, r- (di – 3) = 2.(8) Find the equation of the bisectors of the angles between the linejoining the points with position vectors -3i – 9j. 2i + 3j andthe line meeting the r- and y- axes at the points with positionvectors 3i and 4j.12(9) Find the equation of the line, which is such that the axis of 1bisects the angle between it and the line r · (2i + 5j) = 18.(10) If y = mx bisects an angle between the lines y = m,1, y = m3a,show that(m – m,)(1+ mm,) + (m – m,)(1+ mm,) = 0,and deduce that the two bisectors are given by the roots of theequation(m, + ma)m² + 2(1 – m,mą]m – (m, + m2) = 0.Show that the two values of m given by the above equationdetermine perpendicular lines. Show also that if m, = 1/m,then the bisectors are y =1, y = -1.(11) The position vectors of the vertices of a triangle area = -i+j. b = Ti – 2j. c = 5i + 3j.Find the length of one side of the triangle and the length of thealtitude to that side and hence compute the area of the triangle.

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(18) Find the ratio in which the join of the points A(12, –5) and B(3,4) is cut by the line r (3i – 11j) = 0. Show that the line joining the origin to the point dividing AB externally in the same ratio is perpendicular to the line r- (3i – 11j) = 0.