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

If the direction ratios of two lines are given by \[ l+m+n=0 \] \[ mn-2ln+lm=0 \] then the angle between the lines is

If the direction ratios of two lines are given by \[ l+m+n=0, \qquad mn-2ln+lm=0, \] then the angle between the lines is:

The angle between the lines \[ \frac{x-1}{1} = \frac{y+1}{2} = \frac{z-3}{-1}, \quad \frac{x-1}{2} = \frac{y-3}{3} = \frac{z-1}{4}, \] where \( l, m, n \) are roots of the equation \[ x^2 + x^2 - 4x - 4 = 0, \] is

The values of x for which the angle between $\vec{a}=2x^{2}\hat{i}+4x\hat{j}+\hat{k}$ and $\vec{b}=7\hat{i}-2\hat{j}+x\hat{k}$ is obtuse are}

The values of x for which the angle between $\vec{a}=2x^{2}\hat{i}+4x\hat{j}+\hat{k}$ and $\vec{b}=7\hat{i}-2\hat{j}+x\hat{k}$ is obtuse are}

The acute angle between the lines $x = -2 + 2t, y = 3 - 4t, z = -4 + t$ and $x = -2 - t, y = 3 + 2t, z = -4 + 3t$ is

The direction cosines of the line $x - y + 2z = 5$ and $3x + y + z = 6$ are

The angle between the lines \(3x = 2y = -z\) and \(-x = 6y = -4z\) is

If the two lines given by $ax^2 + 2hxy + by^2 = 0$ make inclinations $\alpha$ and $\beta$, then $\tan(\alpha + \beta) =$

The joint equation of the pair of lines through the origin and making an equilateral triangle with the line $x = 3$ is

If the acute angle between the lines given by $ax^2 + 2hxy + by^2 = 0$ is $\frac{\pi}{4}$, then $4h^2 =$

If the lines $\frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{z-3}{2}$ and $\frac{7-7x}{3\lambda}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles, then $\lambda =$

The angle between the lines, whose direction cosines \( l, m, n \) satisfy the equations \( l + m + n = 0 \) and \( 2l^{2} + 2m^{2} - n^{2} = 0 \), is