JEE Main Three Dimensional Geometry — practice questions
48 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main 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:If $l, m, n$ are the direction cosines of a line, then $l^2+m^2+n^2$ equals:The direction ratios of the line joining the points $(1,2,3)$ and $(4,5,6)$ are:The direction cosines of the x-axis are:Two lines with direction ratios $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$ are perpendicular if:Two lines are parallel if and only if their direction ratios are:The distance between the points $(1,2,3)$ and $(4,5,6)$ is:The direction cosines of a line whose direction ratios are $2,-1,2$ are:The cosine of the angle between two lines with direction ratios $(1,2,2)$ and $(2,2,1)$ is:The cartesian equation of a line through $(x_1,y_1,z_1)$ with direction ratios $a,b,c$ is:A line makes equal angles with the three coordinate axes. Its direction cosines are:A line with direction ratios $(k,2,3)$ is perpendicular to a line with direction ratios $(1,-2,1)$. Then $k$ eThe distance of the point $(2,3,4)$ from the origin is:If a line makes angles $90^\circ, 60^\circ, 30^\circ$ with the x, y, z axes, the sum of squares of its directiThe distance between $(1, 2, 3)$ and $(4, 6, 3)$ in 3D is:The direction cosines of a line with direction ratios $(2, -1, 2)$ are:The plane $2x - y + 3z + 5 = 0$ has normal vector:The distance from $(1, 1, 1)$ to the plane $2x + 2y + z + 3 = 0$ is: