(5) Use vector methods to find the position vectors of the points of intersection of the...

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(5) Use vector methods to find the position vectors of the points of intersection of the following pairs of lines: (a) r (i- j)+2= 0, r (3i +2j) +6 = 0; (b) r (4i – j) - 3 = 0, r (i+2j) = 3; (c) 3x - y+4 =0, 3x – 4y - 15 = 0, (d) 7r - 4y +1= 0, r-y+1= 0. (6) Find the angles of the triangle whose sides are the lines r+2y+ 5 = 0, r- 3y+ 4 = 0 and 3r + y + 7= 0. (7) Find the position vector of the centroid of the triangle formed by the lines r (i - j) – 2 = 0, r (3i+ j) – 10 = 0, r (7i - 3j) – 2 = 0. (8) Find the equation of the line perpendicular to the line 4r- 3y = 0 and passes through the point of intersection of the lines x+ 2y – 5 = 0, 3r - y –1 = 0. 1 (5) Use vector methods to find the position vectors of the points of intersection of the following pairs of lines: (a) r (i- j)+2= 0, r (3i +2j) +6 = 0; (b) r (4i – j) - 3 = 0, r (i+2j) = 3; (c) 3x - y+4 =0, 3x – 4y - 15 = 0, (d) 7r - 4y +1= 0, r-y+1= 0. (6) Find the angles of the triangle whose sides are the lines r+2y+ 5 = 0, r- 3y+ 4 = 0 and 3r + y + 7= 0. (7) Find the position vector of the centroid of the triangle formed by the lines r (i - j) – 2 = 0, r (3i+ j) – 10 = 0, r (7i - 3j) – 2 = 0. (8) Find the equation of the line perpendicular to the line 4r- 3y = 0 and passes through the point of intersection of the lines x+ 2y – 5 = 0, 3r - y –1 = 0. 1