(13) ABCD is a parallelogram. The equations of AB, BC are r (3i - j) +7...

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(13) ABCD is a parallelogram. The equations of AB, BC are r (3i - j) +7 = 0, r (3i- 3j) +5 = 0. Find the position vector of the point D, given that AD passes through the point whose position vector is -8i +3j and CD passes through the point with position vector 5i + 2j. (14) The point A(1, 2) is one vertex of a parallelogram ABCD where side AB lies on the line r (i-2j)+3 = 0 and the diagonal BD lies on the line r (i+ 3j) - 17 0. Given that AD = |BD|. find the position vector of C and the equations of the sides of the parallelogram through C. (15) Show that the lines r (4i + 3j) – 1 = 0, r (-2i+j) -1 = 0, r (i+2j) – 1 = 0 are concurrent. (16) If the lines -2r + 3y = 6, 3r + 5y = 10, 3r- 7y =t are concurrent, find the value of t. (17) Find the equations of the two lines through the point (3,-1) which make an angle with the line 2r – y = 2. (13) ABCD is a parallelogram. The equations of AB, BC are r (3i - j) +7 = 0, r (3i- 3j) +5 = 0. Find the position vector of the point D, given that AD passes through the point whose position vector is -8i +3j and CD passes through the point with position vector 5i + 2j. (14) The point A(1, 2) is one vertex of a parallelogram ABCD where side AB lies on the line r (i-2j)+3 = 0 and the diagonal BD lies on the line r (i+ 3j) - 17 0. Given that AD = |BD|. find the position vector of C and the equations of the sides of the parallelogram through C. (15) Show that the lines r (4i + 3j) – 1 = 0, r (-2i+j) -1 = 0, r (i+2j) – 1 = 0 are concurrent. (16) If the lines -2r + 3y = 6, 3r + 5y = 10, 3r- 7y =t are concurrent, find the value of t. (17) Find the equations of the two lines through the point (3,-1) which make an angle with the line 2r – y = 2.