List of top Mathematics Questions on Coplanarity of Two Lines

A straight line cuts off the intercepts $OA = a$ and $OB = b$ on the positive directions of $x$-axis and $y$ axis respectively If the perpendicular from origin $O$ to this line makes an angle of $\frac{\pi}{6}$ with positive direction of $y$-axis and the area of $\triangle O A B$ is $\frac{98}{3} \sqrt{3}$, then $a^2-b^2$ is equal to :
The lines \(\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-K} \) and \(\frac{x-1}{K}=\frac{y-4}{2}=\frac{z-5}{1} \) are coplanar if :
Let the lines l1: \(\frac{x+5}{3} = \frac{y+4}{1}=\frac{z−α}{−2}\) and l2: 3x + 2y + z – 2 = 0 = x – 3y + 2z - 13 be coplanar. If the point P(a, b, c) on l1 is nearest to the point Q(- 4, -3, 2), then |a| + |b|+|c| is equal to

Let \(\vec{a}, \vec{b}, \vec{c}\)
be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and 
\((\vec{a} \times \vec{b}) \cdot (\vec{b} \times \vec{c}) + (\vec{b} \times \vec{c}) \cdot (\vec{c} \times \vec{a}) + (\vec{c} \times \vec{a}) \cdot (\vec{a} \times \vec{b}) = 168\), then \(|\vec{a}| + |\vec{b}| + |\vec{c}|\)| is equal to :

Two lines:
L₁: \(x = 5, \; \frac{y}{3 - \alpha} = \frac{z}{-2}\)

L₂: \(x = \alpha, \; \frac{y}{-1} = \frac{z}{2 - \alpha}\)

are coplanar. Then \(\alpha\) can take value(s):

Two lines \(L_1:\;x=5,\; \dfrac{y}{3-\alpha}=\dfrac{z}{-2}\) \(L_2:\;x=\alpha,\; \dfrac{y}{1}=\dfrac{z}{2-\alpha}\) are coplanar. Then \(\alpha\) can take value(s)
If vectors \( 2i + j + k \), \( 2j - 3k \), and \( 3i + j + 5k \) are coplanar, then the value of \( a \) is
The perpendicular distance between the lines $9x^2- 24xy + 16y^2 + 21x- 28y+ 10 = 0$ is
$p$ points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is
The perpendicular distance from the point $(1, -1)$ to the line $x + 5y - 9 = 0$ is equal to
The perpendicular distance (d) of a line Ax + By + C = 0 from a point $(x_1, y_1)$ is given by :
The perpendicular bisector of the line segment joining P (1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is
The owner of a milk store finds that he can sell $980\,L$ of milk each week at ?