Question:
The equation of straight line passing through $(a,b,c)$ and parallel to x-axis is:
The equation of straight line passing through $(a,b,c)$ and parallel to x-axis is:
Show Hint
Parallel to axis $\Rightarrow$ only one non-zero direction ratio.
Updated On: Apr 30, 2026
- \(\frac{x-a}{1} = \frac{y-b}{0} = \frac{z-c}{0} \)
- \(\frac{x-a}{0} = \frac{y-b}{1} = \frac{z-c}{1} \)
- \(\frac{x-a}{1} = \frac{y-b}{0} = \frac{z-c}{1} \)
- \(\frac{x-a}{1} = \frac{y-b}{1} = \frac{z-c}{-1} \)
- \(\frac{x-a}{0} = \frac{y-b}{1} = \frac{z-c}{0} \)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
A line parallel to x-axis has direction vector:
\[
(1,0,0)
\]
Step 1: Write symmetric form.
General form: \[ \frac{x-a}{l} = \frac{y-b}{m} = \frac{z-c}{n} \]
Step 2: Substitute direction ratios.
\[ l=1,\; m=0,\; n=0 \] \[ \Rightarrow \frac{x-a}{1} = \frac{y-b}{0} = \frac{z-c}{0} \]
Step 1: Write symmetric form.
General form: \[ \frac{x-a}{l} = \frac{y-b}{m} = \frac{z-c}{n} \]
Step 2: Substitute direction ratios.
\[ l=1,\; m=0,\; n=0 \] \[ \Rightarrow \frac{x-a}{1} = \frac{y-b}{0} = \frac{z-c}{0} \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Equation of a Line in Space Questions
- The vector equation of the straight line $ \frac{1-x}{3}=\frac{y+1}{-2}\,=\frac{3-z}{-1} $
- The line of intersection of the planes \(3x-6y-2z-15=0\) and \(2x=y-2z-5=0\) is ?
- A straight line passing through \( (6,1,3) \) meets the line \( \frac{x-1}{2} = \frac{y}{1} = \frac{z-2}{3} \) at \( Q \). If the lines are perpendicular to each other, then the coordinates of \( Q \) are
- A straight line passes through the points \( (10,8,6) \) and \( (13,9,4) \). A unit vector parallel to this line is
- The equation of a line passing through $(-1,2,-4)$ and parallel to the straight line $\dfrac{-x-1}{4} = \dfrac{2y+1}{-1} = \dfrac{-z+4}{3}$, is:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions