TS EAMCET Three Dimensional Geometry — practice questions
78 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAMCET Three Dimensional Geometry in the app →The distance between two points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$ in three-dimensional space is:The direction cosines of a line are $l$, $m$, $n$. They satisfy:A line passes through the points $(1, 2, 3)$ and $(4, 6, 9)$. The direction ratios of the line are:In 3D, distance between points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂):Direction cosines (l, m, n) of a line satisfy:Equation of line through point (x₀, y₀, z₀) with direction (a, b, c):Two lines are parallel if their direction ratios are:Normal vector to plane ax + by + cz = d is:Distance from point (1, 2, 3) to plane x + y + z = 0:Find equation of plane through (1, 0, 0), (0, 2, 0), (0, 0, 3):Two planes are perpendicular if:Vector form of line: r = a + λ b where:Coplanar lines have:Equation of sphere with center (h, k, l) and radius r:Angle between line and plane: if direction of line is L and normal to plane is N, sin(angle line-plane):Projection of vector a on b:Skew lines in 3D are:Distance between two parallel planes 2x + y + z = 5 and 2x + y + z = 10:Find equation of plane perpendicular to (1, 2, 3) passing through (4, 5, 6):Angle θ between two planes 2x + 3y + 4z = 0 and x + y + z = 0:Three points (1,0,0), (0,1,0), (0,0,1) are vertices of a triangle. Area:Plane passing through origin and perpendicular to line (x-1)/2 = (y-2)/3 = (z-3)/-1:Foot of perpendicular from point (3, 1, 2) to plane x + y + z = 6:Direction ratios of normal to plane 2x - y + 3z + 7 = 0:For a line with direction cosines l, m, n, the angles it makes with axes are:Coordinates of foot of perpendicular from point (1, 2, 3) to x-axis:Equation of straight line passing through two points A(1,2,3) and B(4,5,6):3D analog of Pythagoras: for a box with sides a, b, c, the body diagonal is:What are the direction cosines of the y-axis?A line makes angles 90, 60 and 30 degrees with the x, y, z axes. Its direction cosines are:A line has direction ratios 2, -1, -2. One set of its direction cosines is:Reversing the direction of a directed line in space makes its direction cosines:When a directed line is reversed, each direction angle is replaced by its:Two parallel lines drawn in the same sense in space have:How many sets of direction ratios does a line in space have?A line makes equal acute angles with all three axes. Each of its direction cosines is:The points (2, 3, 4), (-1, -2, 1) and (5, 8, 7) are:Direction ratios of the segment from (1, 2, 3) to (4, 6, 15) are:A line through (x1, y1, z1) with direction ratios a, b, c has Cartesian form:The line through (5, 2, -4) parallel to 3i + 2j - 8k has Cartesian form:A line passes through (1, 2, 3) parallel to 3i + 2j - 2k. Which point lies on it?On the line r = 2i - j + 4k + λ(i + 2j - k), the point for λ = 2 is:In r = a + λb, the vector b represents the line's:In the equation r = a + λb of a line, the vector a is the position vector of:A line in space is uniquely fixed when it passes through:A line through (1, 2, 3) and (3, 4, 5) has direction ratios proportional to:Which point lies on the line through the origin parallel to the x-axis?Lines with direction ratios (a1, b1, c1) and (a2, b2, c2) are perpendicular when:The lines with direction vectors i + 2j + 2k and 3i + 2j + 6k have cos θ equal to:Lines with direction ratios 3, 5, 4 and 1, 1, 2 meet at an angle whose cosine is:Two lines have direction ratios 1, 1, 0 and 0, 1, 1. They are inclined at:For which k are lines with ratios (k, 2, 3) and (1, -1, 2) perpendicular?The angle between two lines in space is conventionally taken as:Skew lines in space are lines that are:Which statement is true of every pair of skew lines?The shortest distance between two parallel lines is the:For r = a1 + λb1 and r = a2 + μb2 (skew), the shortest distance is:Shortest distance between r = i + j + λ(2i - j + k) and r = 2i + j - k + μ(3i - 5j + 2k):The parallel lines r = i + 2j - 4k + λ(2i + 3j + 6k) and r = 3i + 3j - 5k + μ(2i + 3j + 6k) are how far apart?How far apart are the parallel lines r = λi and r = 3j + 4k + μi?What is the shortest distance between the x-axis and the line through (0, 0, 4) parallel to the y-axis?Two parallel lines in space are always:If two lines lie in the same plane, they must either cross or be:Direction cosines of a vector are the cosines of its angles with the:Which triple can be the direction cosines of a line?If a line has l = 1/2 and m = 1/2, then n equals:A line has direction cosines 0, 1/2 and n. What is n?A line makes 60 degrees with the x-axis and 60 degrees with the y-axis. It can make which angle with the z-axiDirection ratios of line PQ are 2, -3, 4. Those of QP can be:An undirected line in space has how many sets of direction cosines?To find the direction cosines of a line missing the origin, we draw through the origin a line that is:Direction ratios a, b, c relate to cosines l, m, n by a = λl, where λ is:Which point lies on the line through (1, 2, 3) with direction (3, 1, -4)?The line (x-1)/2 = (y+3)/4 = (z-5)/6 has direction cosines:Line through (1, -1, 2) and (3, 4, -2), and line through (0, 3, 2) and (3, 5, 6), are:Lines with ratios a, b, c and b-c, c-a, a-b are inclined at:If (b1 x b2) . (a2 - a1) = 0 for two lines, the lines are:A unit vector along the common perpendicular of lines with directions b1, b2 is: