Question:
A line makes the same angle θ with each of the X and Z-axes. If the angle β, which it makes with Y-axis, is such that sin²β=3sin²θ, then cos²θ equals
A line makes the same angle θ with each of the X and Z-axes. If the angle β, which it makes with Y-axis, is such that sin²β=3sin²θ, then cos²θ equals
Show Hint
Use direction cosine identity l²+m²+n²=1.
Updated On: Mar 20, 2026
- \(2/5\)
- \(1/5\)
- \(3/5\)
- 2/3
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Let direction cosines be l=n=cosθ, m=cosβ.
l²+m²+n²=1 ⟹ 2cos²θ+cos²β=1
sin²β=1-cos²β=3(1-cos²θ)
Solving gives cos²θ=(3)/(5).
Was this answer helpful?
0
0
Top BITSAT Mathematics Questions
- The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ is
- If one root of the quadratic equation $a x^{2}+b x+c=0$ is equal to $n^{\text {th }}$ power of the other root, then the value of: $a^{\frac{n}{n-1}} C^{\frac{1}{n-1}}+c^{\frac{n}{n-1}} a^{\frac{1}{n-1}}$ is equal to
- $(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to
- An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is
- $2^{1/4}. 2^{2/8}. 2^{3/16}. 2^{4/32}......\infty$ is equal to-
View More Questions
Top BITSAT introduction to three dimensional geometry Questions
- The ratio in which the line joining the points \( (2,1,5) \) and \( (3,4,3) \) is divided by the plane \( x + y - z = \dfrac{1}{2} \) is:
- If the line through the points A(k,1,-1) and B(2k,0,2) is perpendicular to the line through the points B and C(2+2k,k,1), then the value of k is
- A line makes the same angle \(\theta\) with each of the X and Z-axes. 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
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions