BITSAT Three Dimensional Geometry — practice questions
31 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice BITSAT 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:The point that divides the line segment joining $A(x_1, y_1, z_1)$ and $B(x_2, y_2, z_2)$ internally in the raThe angle between two lines with direction cosines $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$ satisfies:A line passes through the points $(1, 2, 3)$ and $(4, 6, 9)$. The direction ratios of the line are:The equation of a plane in normal form is $\vec{r} \cdot \hat{n} = d$, where $\hat{n}$ is a unit vector normalIn 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: