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REVISION SET- 09, , CLASS – XII, SUB – MATH, , TIME – 1.30 Hrs., F.M. – 100, , 1) If r = 2 i – 3 j – 2 k, find the direction cosines of r ., 2) Find the direction cosines of the line joining the points P (4, 3, -5) and Q (-2, 1, -8 ) ?, 3) Determine the value of k so that the line joining the points A (k,1,-1) and B (2, 0, 2k) is perpendicular, to the line joining the point C (4, 2k, 1) and D (2, 3, 2)., 4) Find the projection of the line segment joining (2, -1, 3) and (4, 2, 5) on a line which makes equal, acute angles with co-ordinate axes., 5) Find the angle between the following pair of lines., 𝑥, 𝑦, 𝑧, 𝑥−5 𝑦 −2 𝑍−3, = 2 = 1 and 4 = 1 = 8, 2, 6) Find the value of p so that the lines., 1−𝑥 7𝑦−14 𝑍−3, 7−7𝑥 𝑦 −5 6− 𝑍, =, =, and, = 1 = 5 are at right angles., 3, 2𝑝, 2, 3𝑝, 7) Find the foot and length the perpendicular from point (2, -1, 5) to the line, , 𝑥−11, 10, , =, , 𝑦+2, , 8) Find the equation of the perpendicular drawn from the point (2, 4, -1) to the line, , −4, 𝑥+5, 1, , 𝑍+8, , = −11 ., =, , 𝑦 +3, 4, , =, , 𝑍−6, −9, , ., , 9) Find the shortest distance between the following pair of lines., 𝑥−3 𝑦−5 𝑍−7, 𝑥+1 𝑦 +1 𝑍+1, =, =, and, =, =, 1, , −2, , 1, , 7, , −6, , 1, , 10) Find the vector equation of a plane which is at a distance of 7 units from the origin and normal, to the vector 3 i + 5 j – 6 k ., 11) Find the equation of the plane through (3, 4, -1) which is parallel to the plane, r . (2 i – 3 j + 5 k ) + 7 = 0., 12) Find the equation of the plane passing through the point (3, -3, 1) and perpendicular to the line, Joining (3, 4, -1) and (2, -1, 5) ., 13) Find the equation of the plane through the point (1, 4, -2) and parallel to the plane -2x + y–3z = 7., 𝑥+1 𝑦, 𝑍−3, 14) Find the angle between the line 2 = 3 = 6 and the plane 10x + 2y – 11z = 3., 15) Find the vector equation of the plane through the line of intersection of the planes, r . (2 i + 2 j - 3 k) = 7, r . (2 i + 5 j + 3 k) = 9 and through the point (2, 1, 3)., 16) Find the distance of the point (-1, -5, -10) from the point of intersection of the line, r = 2 i – j + 2 k + 𝜆 (3 i + 4 j + 2 k) and the plane r . ( i – j + k ) = 5., 17) Find the co-ordinates of the foot of perpendicular drawn from origin to the following planes., x + y + z =1, 𝑥+1, 𝑦 +2, 𝑧+3, 18) Find the co-ordinates of the point where the line 2 = 3 = 4 , meets the plane x+y+4z = 6., 19) Show that the lines, , 𝑥+3, −3, , =, , 𝑦 −1, 1, , =, , 𝑧−5, 5, , and, , 𝑥+1, −1, , =, , 𝑦 −2, 2, , =, , 𝑧−5, 5, , are coplanar., , 20) Find the distance between the planes 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12.