List of top Mathematics Questions on Coplanarity of Two Lines asked in MHT CET

If for some \(m\in R\) the lines \(L_1:\frac{x+1}{m} = \frac{y-m}{-1} = \frac{z-1}{1}\) and \(L_2:\frac{x+2}{-4} = \frac{y+1}{9} = \frac{z+1}{1}\) are coplanar, then line \(L_1\) passes through the point

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

If the lines \(x = -1+s\), \(y = 3-λs\), \(z = 1+λs\) and \(x = \frac{t}{2}\), \(y = 1+t\), \(z = 2-t\) with parameters s and t, are coplanar, then \(λ =\)

If the lines \(\overset{⃗}{r} = (\hat{i}+m\hat{j}+3\hat{k})+λ(2\hat{i}+3\hat{j}+4\hat{k})\) and \(\overset{⃗}{r} = (4\hat{i}+\hat{j})+μ(5\hat{i}+m\hat{j}+\hat{k})\) intersect each other, then m =

If the lines \(\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}\) and \(\frac{x-3}{1} = \frac{y-c}{2} = \frac{z}{1}\) intersect, then the radius of circle \(x^2+y^2-4x+10y+c = 0\) is

If the lines \(\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}\) and \(\frac{x-2}{1} = \frac{y+m}{2} = \frac{z-2}{1}\) intersect each other, then the value of \(m\) is....

If the lines $x = ay - 1 = z - 2$ and $x = 3y - 2 = bz - 2$ ($ab \neq 0$) are coplanar, then \dots

The lines $\frac{x-3}{1} = \frac{y-2}{1} = \frac{z-5}{-k}$ and $\frac{x-4}{k} = \frac{y-3}{1} = \frac{z-3}{2}$ are coplanar, hence $k =$}

If the vectors \(m\hat{i} + m\hat{j} + n\hat{k}, \hat{i} + \hat{k}, n\hat{i} + n\hat{j} + p\hat{k}\) lie in a plane then...

The lines $\frac{x-3}{1} = \frac{y-2}{1} = \frac{z-5}{-k}$ and $\frac{x-4}{k} = \frac{y-3}{1} = \frac{z-3}{2}$ are coplanar, hence $k =$}

If the vectors $2\hat{i} - \hat{j} - \hat{k}$, $\hat{i} + 2\hat{j} - 3\hat{k}$ and $3\hat{i} + \lambda\hat{j} + 5\hat{k}$ are coplanar, then the value of $\lambda$ is