List of top Mathematics Questions on Equation of a Line in Space asked in MHT CET

The lines \( \vec{r} \times \vec{a} = \vec{b} \times \vec{a} \) and \( \vec{r} \times \vec{b} = \vec{a} \times \vec{b} \) intersect at a point, where \( \vec{a} = \hat{i} + \hat{j} \) and \( \vec{b} = \hat{i} - \hat{k} \). Find the point of intersection.

Identify the co-ordinates of the point where the line joining \( (1,1,1) \) and \( (2,2,2) \) intersects the plane \( x+y+z=9 \).

The line passing through the point \( (5, 1, a) \) and \( (3, b, 1) \) crosses the yz-plane at \( (0, \frac{17}{2}, \frac{-13}{2}) \), then the value of \( 2a + 3b \) is:

If the line $\frac{x-3}{2} = \frac{y+5}{1} = \frac{z+2}{2}$ lies in the plane $\alpha x + 3y - z + \beta = 0$, then values of $\alpha$ and $\beta$ respectively are \dots}

The altitude through vertex A of $\triangle ABC$ with position vectors of points A, B, C as $\vec{a}, \vec{b}, \vec{c}$ respectively is ______.

A triangle ABC is formed by A(1, -1, 0), B(3, 5, 3), C(-11, -5, 6). The equation of the internal angle bisector of angle A is ______.

The line $\frac{x-1}{2}=\frac{y+2}{-1}=\frac{z}{1}$ intersects the XY and YZ planes at A and B. The line through A and B is}

The line $\frac{x-1}{2}=\frac{y+2}{-1}=\frac{z}{1}$ intersects the XY and YZ planes at A and B. The line through A and B is}

The lines $\frac{6x-6}{18}=\frac{y+1}{3}=\frac{z-1}{5}$ and $\frac{3x+6}{12}=\frac{y-1}{3}=\frac{z+1}{2}$ are...

The lines $\frac{6x-6}{18}=\frac{y+1}{3}=\frac{z-1}{5}$ and $\frac{3x+6}{12}=\frac{y-1}{3}=\frac{z+1}{2}$ are...

The equation of a line passing through the point $(-1, 2, 3)$ and perpendicular to the lines $\frac{x}{2} = \frac{y-1}{-3} = \frac{z+2}{-2}$ and $\frac{x+3}{-1} = \frac{y+3}{2} = \frac{z-1}{3}$ is

The number of solutions of \(16^{\sin^2 x} + 16^{\cos^2 x} = 10\) in \(0 \le x \le 2\pi\) are

The equation of a line passing through the point $(-1, 2, 3)$ and perpendicular to the lines $\frac{x}{2} = \frac{y-1}{-3} = \frac{z+2}{-2}$ and $\frac{x+3}{-1} = \frac{y+3}{2} = \frac{z-1}{3}$ is

The equation of a line passing through the point $(-1, 2, 3)$ and perpendicular to the lines $\frac{x}{2} = \frac{y-1}{-3} = \frac{z+2}{-2}$ and $\frac{x+3}{-1} = \frac{y+3}{2} = \frac{z-1}{3}$ is

If the Cartesian equation of a line is $6x-2=3y+1=2z-2$, then the vector equation of the line is

If the lines $\frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-3}{1} = \frac{y-\frac{9}{2{2} = \frac{z}{1}$ intersect, then the value of k is

The Cartesian equation of a line is $3x + 1 = 6y - 2 = 1 - z$, then its vector equation is

The vector equation of the line whose Cartesian equations are $y = 2$ and $4x - 3z + 5 = 0$ is

A line drawn from a point $A(-2,-2,3)$ and parallel to the line $\frac{x}{-2} = \frac{y}{2} = \frac{z}{-1}$ meets the $YOZ$ plane in point $P$, then the coordinates of the point $P$ are

The vector equation of the line passing through $\text{P}(1,2,3)$ and $\text{Q}(2,3,4)$ is

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 equation of a line passing through $(3, -1, 2)$ and perpendicular to the lines $\bar{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda (2\hat{i} - 2\hat{j} + \hat{k})$ and $\bar{r} = (2\hat{i} + \hat{j} - 3\hat{k}) + \mu (\hat{i} - 2\hat{j} + 2\hat{k})$ is

The vector equation of the line whose Cartesian equations are $y = 2$ and $4x - 3z + 5 = 0$ is

The Cartesian equation of the line passing through the points A(2, 2, 1) and B(1, 3, 0) is