TS EAMCET Coordinate Geometry: Direction Cosines and Direction Ratios — practice questions
48 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAMCET Coordinate Geometry: Direction Cosines and Direction Ratios in the app →A line is equally inclined to all three coordinate axes. Its direction cosines areDirection ratios 3, 4, 12 give direction cosines (positive sign)The direction cosines of a line with direction ratios 6, 2, 3 areA line joins (1, 2, 3) and (4, 6, 15). Its direction cosines areDirection ratios of the line through (1, 2, 3) and (3, 5, 9) can be taken asA line through the origin makes 60° with both the x and y axes. Its acute angle with the z-axis isReversing a directed line replaces its direction angles α, β, γ by theirTwo parallel lines have direction cosines that areDirection ratios are also known by the nameWhich triple is NOT a set of direction ratios of the line with ratios 1, 2, 3?For A(2, 3, -4) and B(1, -2, 3), direction ratios of AB can beThree points are collinear if the lines joining two pairs of them haveThe vector i + j + k makes an angle with the x-axis whose cosine isThe x-axis and the y-axis meet at an angle whose cosine isDirection cosine l for ratios a, b, c is given by l =For ratios 1, -2, -2, the direction cosines with positive first entry areAngles α, β, γ that a directed line makes with the axes are calledFor any line, sin²α + sin²β + sin²γ equalsDirection cosines of line joining (1,2,3), (3,6,7):Ratios of segment (2,3,5) to (5,7,1) may be:Reversing a line with cosines 1/3, 2/3, 2/3 gives:Another name some authors use for direction ratios is:Find k so that (1, 2, 3), (2, 4, 5) and (4, 8, k) are collinear.AB has ratios 1,-2,3 and BC has -2,4,-6. A, B, C are:Angle between ratios 1,-1,2 and -2,2,-4 is:Cosine of the angle between x-axis and y-axis is:Ratios 3, 4, 0 and the x-axis: cosine of the angle is:Origin to (1,1,1) with the x-axis: the cosine is:Ratios 2, -1, -2 give n (positive k) equal to:A line perpendicular to the x-axis has l equal to:If n = 0 for a line, its angle with the z-axis is:Ratios that fit cosines 2/7, 3/7, 6/7:Ratios 2, 3, 6: the sum l + m + n (positive) is:Cosines of origin to (-1, 2, -2) line:A line has direction cosines l = 1/2 and m = 1/2. A possible value of n is:If a, b, c are the direction angles of a line, then sin^2 a + sin^2 b + sin^2 c equals:A segment joins (2, -1, 4) and (5, 3, -8). Its length is:Lines with direction ratios (2, k, 6) and (1, -3, 3) are parallel. The value of k is:A line has direction cosines (1/3, 2/3, 2/3) and another has (2/3, 1/3, -2/3). The angle between them is:The cosine of the angle between two body diagonals of a cube is:The direction angles of a vector lie in which range?A vector of magnitude 10 has direction cosines (3/5, 0, 4/5). Its components are:A vector of length 6 lies along direction cosines (1/3, 2/3, 2/3). Its z-component is:A line with direction ratios 1, -1, sqrt(2) makes what acute angle with the z-axis?Which set can be direction ratios of the x-axis?A line is perpendicular to both the x-axis and the y-axis. Its direction cosines are:A line makes acute angles of 60 degrees with the x and y axes. Its angle with the z-axis is:Direction cosines give an easy way to represent which feature of a vector in Cartesian space?