New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2004 · Shift 0 · Q96

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
3D Geometry
2004 · Shift 0 · Q96

3D Geometry question

2004 · Shift 0 · Q96

JEE MainMathematics3D GeometryMCQ+4 / −1

A line makes the same angle

\theta

, with each of the

x

and

z

axis. If the angle

\beta \,

, which it makes with y-axis, is such that

\,{\sin ^2}\beta = 3{\sin ^2}\theta ,

then

{\cos ^2}\theta

equals :

A
${2 \over 5}$
B
${1 \over 5}$
C
${3 \over 5}$
D
${2 \over 3}$

More from 3D Geometry

The two lines $x = a y + b, z = cy + d$ and $x = a^{'} y + b^{'}, z = c^{'} y + d^{'}$ will be perpendicular, if and only if :2003 · MCQ
The lines $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k}$ and $\frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z - 5}{1}$ are coplanar if :2003 · MCQ
Let the vertices Q and R of the triangle PQR lie on the line $\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}, QR = 5$ and the coordinates of the point $P$ be $(0, 2, 3)$ . If the area of the triangle $P QR$ is $\frac{m}{n}$ then :2025 · MCQ
Let $A B C D$ be a tetrahedron such that the edges $A D$ and $A D$ are mutually perpendicular. Let the areas of the triangles $ABC, ACD$ and ADB be 5,6 and 7 square units respectively. Then the area (in square units)…2025 · MCQ
If the image of the point $P (1, 0, 3)$ in the line joining the points $A (4, 7, 1)$ and $B (3, 5, 3)$ is $Q (α, β, γ)$ , then $α + β + γ$ is equal to :2025 · MCQ
The line $L_{1}$ is parallel to the vector $a = - 3 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and passes through the point $(7, 6, 2)$ and the line $L_{2}$ is parallel to the vector $b = 2 \hat{i} + \hat{j} + 3 \hat{k}$ …2025 · MCQ
Let a line passing through the point $(4, 1, 0)$ intersect the line $L_{1} : \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ at the point $A (α, β, γ)$ and the line $L_{2} : x - 6 = y = - z + 4$ at the point $B (a, b, c)$ . Then $1 α a 0 β b 1 γ c$ …2025 · MCQ
Line $L_{1}$ passes through the point $(1, 2, 3)$ and is parallel to $z$ -axis. Line $L_{2}$ passes through the point $(λ, 5, 6)$ and is parallel to $y$ -axis. Let for $λ = λ_{1}, λ_{2}, λ_{2} < λ_{1}$ , the shortest…2025 · MCQ