List of top Mathematics Questions on angle between two lines asked in KEAM

The direction ratios of a straight line \(L_1\) are 2,-1,2 and that of another straight line \(L_2\) are 3,6,-2. Then the angle between \(L_1\) and \(L_2\) is
The straight line passing through the points $(3,2,3)$ and $(5,-1,-2)$ is perpendicular to the straight line passing through the points $(1,3,1)$ and $(\alpha, \alpha, \alpha)$. Then the value of $\alpha$ is equal to
If the straight line passing through the points $(1,-1,2)$ and $(3,2,8)$ makes angle $\beta$ with the $y$-axis, then the value of $\cos \beta$ is equal to
The angle between the lines $\vec{r}=(3+\alpha)\hat{i}+2(1+\alpha)\hat{j}+2(-2+\alpha)\hat{k}$ and $\vec{r}=(5+3\beta)\hat{i}+2(1+\beta)\hat{j}+6\beta\hat{k}$ , where $\alpha$ and $\beta$ are parameters, is
A straight line through the point (1,-1,0) meets the line $\frac{x-1}{1}=\frac{y+1}{1}=\frac{z-1}{-1}$ at right angle. Its equation is ________.
The angle between the lines \( \frac{x-3}{1} = \frac{y+1}{-1} = \frac{z-2}{-1} \) and \( \frac{x+1}{2} = \frac{y-2}{2} = \frac{z+3}{-2} \) is
The angle between the lines $\dfrac{x-3}{-4} = \dfrac{y+2}{3} = \dfrac{z-1}{5}$ and $\dfrac{x-2}{2} = \dfrac{y-4}{1} = \dfrac{z+3}{3}$ is
The angle between the pair of lines \( \frac{x-2}{2} = \frac{y-1}{5} = \frac{z+3}{-3} \) and \( \frac{x+2}{-1} = \frac{y-4}{8} = \frac{z-5}{4} \) is:
If the two lines $\frac{x-1}{2} = \frac{1-y}{-a} = \frac{z}{4}$ and $\frac{x-3}{1} = \frac{2y-3}{4} = \frac{z-2}{2}$ are perpendicular, then the value of $a$ is equal to:
The angle between the lines \( 2x = 3y = -z \) and \( 6x = -y = -4z \) is
Equation of the line through the point (2, 3, 1) and parallel to the line of intersection of the planes \( x - 2y - z + 5 = 0 \) and \( x + y + 3z = 6 \) is:
Equation of the line through the point (2, 3, 1) and parallel to the line of intersection of the planes \( x - 2y - z + 5 = 0 \) and \( x + y + 3z = 6 \) is:
Equation of the line through the point (2, 3, 1) and parallel to the line of intersection of the planes \( x - 2y - z + 5 = 0 \) and \( x + y + 3z = 6 \) is: