List of top Mathematics Questions on angle between two lines

The angle between the planes \( \vec{r} \cdot (12\hat{i} + 4\hat{j} - 3\hat{k}) = 5 \) and \( \vec{r} \cdot (5\hat{i} + 3\hat{j} + 4\hat{k}) = 7 \) is:
The measure of the angle between the lines $ x = k + 1, \quad y = 2k - 1, \quad z = 2k + 3, \quad k \in \mathbb{R} $ and $ \frac{x-1}{2} = \frac{y+1}{1} = \frac{z-1}{2} $ is:

The sine of the angle between the straight line $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{4-z}{5}$ and the plane $2x - 2y + z = 5$ is:

The angle between the line $x + y = 3$ and the line joining the points $(1, 1)$ and $(-3, 4)$ is:
If the angle between the lines given by the equation \(x^2 -3xy + dy^2 + 3x - 5y + 2=0\); \(d > 0\), is \(tan^{-1} (\frac{1}{a})\) then the value of d is?
The angle between the lines \( 2x = 3y - z \) and \( 6x = -y - 4z \) is:
The angle between the lines $2x = 3y = - z$ and $6x = - y = - 4z$ is
The angle between two diagonals of a cube is
The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0 $ and $ l^2= m^2 + n^2 $is
The angle between the pair of lines $ ({{x}^{2}}+{{y}^{2}}){{\sin }^{2}}\alpha ={{(x\,\cos \theta -y\,\sin \theta )}^{2}} $ is :
The area of the triangle whose vertices are $A = (1, -1, 2), B = (2, 1, -1)$ and $C = (3, -1, 2)$ is

in the given figure AB | | CD, Find the value of x.

AB | | CD

The angle between the pair of tangents drawn from the point (1, 2) to the ellipse $3x^2 + 2y^2 = 5 $ is
The angle between two lines $\frac{x+1}{2} = \frac{y+3}{2} = \frac{z-4}{-1} $ and $\frac{x-4}{1} = \frac{y+4}{2} = \frac{z+1}{2} $ is :