
A point $(x,y,z)$ moves parallel to $x$-axis. Which of the three variables $x$, $y$, $z$ remains fixed?
A. $x$
B. $y$ and $z$
C. $x$ and $y$
D. $z$ and $x$
Answer
162.3k+ views
Hint: A line parallel to the $x$-axis has an equation of the type $y = b$ , $z = c$ , which intersects the $y - z$ axis at the position $(0,b,c)$ . These lines are parallel to the $x$-axis and parallel to it at a distance of $b$, $c$ units. Since it is parallel to the $x$-axis, the slope of the equation for the line is zero.
Formula Used: Direction cosines can be expressed as:
$l = \cos \alpha $ , $m = \cos \beta $ and $n = \cos \gamma $ .
Complete step-by-step solution:
Firstly, we would find the direction cosines of a line parallel to the $x$-axis. As we are familiar with the concept of direction cosines and direction ratios. The cosine of the angles that a line is making with the $x$-axis, $y$-axis and $z$-axis i.e., $\cos \alpha $ , $\cos \beta $ and $\cos \gamma $ , respectively.

As the line is parallel to the $x$-axis, it will make angle $0^\circ $ with the $x$-axis. Similarly, it will form an angle of $90^\circ $ with the other two axes i.e., $y$-axis and $z$-axis.
So, we have $\alpha = 0^\circ $, $\beta = \gamma = 90^\circ $
Hence, direction cosines are
$l = \cos 0^\circ = 1$
$m = n = \cos 90^\circ = 0$
So, we will get the equation of $x$-axis
$y = 0$ and $z = 0$ . Hence, $y$ and $z$ remain fixed.
So, the correct option will be B.
Note: As in this question, where we were required to determine the equation of a line that was parallel to $x$-axis and passes through the point $(x,y,z)$ , it is obvious that the only axes we will be considering are $y$ and $z$ . A straight line that is parallel to the $x$-axis will always have a slope of zero since there is no slope for a line that is parallel to an axis.
Formula Used: Direction cosines can be expressed as:
$l = \cos \alpha $ , $m = \cos \beta $ and $n = \cos \gamma $ .
Complete step-by-step solution:
Firstly, we would find the direction cosines of a line parallel to the $x$-axis. As we are familiar with the concept of direction cosines and direction ratios. The cosine of the angles that a line is making with the $x$-axis, $y$-axis and $z$-axis i.e., $\cos \alpha $ , $\cos \beta $ and $\cos \gamma $ , respectively.

As the line is parallel to the $x$-axis, it will make angle $0^\circ $ with the $x$-axis. Similarly, it will form an angle of $90^\circ $ with the other two axes i.e., $y$-axis and $z$-axis.
So, we have $\alpha = 0^\circ $, $\beta = \gamma = 90^\circ $
Hence, direction cosines are
$l = \cos 0^\circ = 1$
$m = n = \cos 90^\circ = 0$
So, we will get the equation of $x$-axis
$y = 0$ and $z = 0$ . Hence, $y$ and $z$ remain fixed.
So, the correct option will be B.
Note: As in this question, where we were required to determine the equation of a line that was parallel to $x$-axis and passes through the point $(x,y,z)$ , it is obvious that the only axes we will be considering are $y$ and $z$ . A straight line that is parallel to the $x$-axis will always have a slope of zero since there is no slope for a line that is parallel to an axis.
Recently Updated Pages
If there are 25 railway stations on a railway line class 11 maths JEE_Main

Minimum area of the circle which touches the parabolas class 11 maths JEE_Main

Which of the following is the empty set A x x is a class 11 maths JEE_Main

The number of ways of selecting two squares on chessboard class 11 maths JEE_Main

Find the points common to the hyperbola 25x2 9y2 2-class-11-maths-JEE_Main

A box contains 6 balls which may be all of different class 11 maths JEE_Main

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

NIT Cutoff Percentile for 2025

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Degree of Dissociation and Its Formula With Solved Example for JEE

Free Radical Substitution Mechanism of Alkanes for JEE Main 2025
