JEE MAIN Straight Line Previous Year Questions (PYQs) – Page 4 of 13

Let the image of the point $(1,0,7)$ in the line $\dfrac{x}{1}=\dfrac{y-1}{2}=\dfrac{z-2}{3}$ be the point $(\alpha,\beta,\gamma)$. Then which one of the following points lies on the line passing through $(\alpha,\beta,\gamma)$ and making angles $\dfrac{2\pi}{3}$ and $\dfrac{3\pi}{4}$ with the $y$-axis and $z$-axis respectively, and an acute angle with the $x$-axis?

If in a parallelogram $ABDC$, the coordinates of $A, B$ and $C$ are respectively $(1,2)$, $(3,4)$ and $(2,5)$, then the equation of the diagonal $AD$ is :

If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x - 8 and y = mx + c is at (3, -1), then m - c is :

Let the points $\left(\dfrac{11}{2},,\alpha\right)$ lie on or inside the triangle with sides $x+y=11$, $x+2y=16$ and $2x+3y=29$. Then the product of the smallest and the largest values of $\alpha$ is equal to:

Let $R$ be the interior region between the lines $3x - y + 1 = 0$ and $x + 2y - 5 = 0$ containing the origin. The set of all values of $a$, for which the points $(a^2,\,a+1)$ lie in $R$, is:

Let a variable line of slope $m>0$ passing through $(4,-9)$ intersect the coordinate axes at points $A$ and $B$. The minimum value of the sum of the distances of $A$ and $B$ from the origin is:

A straight line through a fixed point $(2,3)$ intersects the coordinate axes at distinct points $P$ and $Q$. If $O$ is the origin and the rectangle $OPRQ$ is completed, then the locus of $R$ is :

The intersection of three lines x - y = 0, x + 2y = 3 and 2x + y = 6 is a

The shortest distance between the lines $\dfrac{x+2}{1}=\dfrac{y}{-2}=\dfrac{z-5}{2}$ and $\dfrac{x-4}{1}=\dfrac{y-1}{2}=\dfrac{z+3}{0}$ is:

An ordered pair ($\alpha $, $\beta $) for which the system of linear equations
(1 + $\alpha $) x + $\beta $y + z = 2
$\alpha $x + (1 + $\beta $)y + z = 3
$\alpha $x + $\beta $y + 2z = 2
has a unique solution, is :