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

The Cartesian equations of the line passing through \(A(0,1,1)\) and parallel to the X-axis are ....

A line passing through the points \((1,-1,2)\) and \((2,0,1)\) meets the XY plane and the YZ plane at points A and B respectively. The distance AB is equal to...

The symmetric form of the equation of the line \(x = ay+b\), \(z = cy+d\) is

The line \(\ell\) passes through the point \((2,1,1)\) and is parallel to the plane \(x+y+2z = 18\). If line \(\ell\) intersects the line \(\frac{x+2}{3} = \frac{y+1}{-1} = \frac{z-2}{1}\), then equation of the line \(\ell\) is...

The equation of the perpendicular line from the point \((2,-3,1)\) to the line \(\frac{x+1}{2} = \frac{y-3}{3} = \frac{z+2}{-1}\) is

The angle between the line \(x-1 = 2-y = \frac{2z-6}{4}\) and the plane \(\overset{⃗}{r}\cdot (2\hat{i}+\hat{j}+\hat{k}) = 10\) is

The sum of the coordinates of one of the points on the line \(\frac{x-2}{1} = \frac{y+3}{-2} = \frac{z+5}{2}\) which is at a distance of 3 units from the point \((2,-3,-5)\) is ...

If the lines \(\overset{⃗}{r} = \hat{i}+\hat{j}-\hat{k}+λ(q\hat{i}-2\hat{j}+\hat{k})\) and \(\overset{⃗}{r} = p\hat{i}-3\hat{j}+2\hat{k}+μ(\hat{i}-2\hat{j}+2\hat{k})\) intersect each other and \(q\hat{i}-2\hat{j}+\hat{k}\) is collinear to \(4\hat{i}-4\hat{j}+2\hat{k}\), then the values of \(p\) and \(q\) are

The equation of a line in cartesian form passing through (0, 0, 0) and (4, 3, c) and parallel to \(\overset{⃗}{a}\times \overset{⃗}{b}\) where \(\overset{⃗}{a} = 2\hat{i}+\hat{j}+2\hat{k}\), \(\overset{⃗}{b} = 3\hat{i}-4\hat{j}\) is

The vector equation of the line whose cartesian equations are \(x = 2,2y-3z+7 = 0\)

The co-ordinates of the point where the line joining the points \((3,5,-7)\) and \((-2,1,8)\) is intersected by the YOZ plane are

If the lines \(\frac{x-5}{5m+2} = \frac{2-y}{5} = \frac{1-z}{-1}\) and \(x = \frac{2y+1}{4m} = \frac{1-z}{-3}\) are perpendicular to each other, then the value of m is ...

The equation of a line passing through a point \((4,-2,3)\) and perpendicular to the XZ-plane is....

The point having position vector \(4\hat{i}-11\hat{j}+2\hat{k}\) lies on the line

The point of intersection of the two lines \(\frac{x-3}{3} = \frac{y-3}{-1},z-1 = 0\) and \(\frac{x-6}{2} = \frac{z-1}{3},y-2 = 0\) is....

If \(\overset{̄}{a} = \hat{i}+\hat{j}\) and \(\overset{̄}{b} = \hat{i}-\hat{k}\), then the point of intersection of the lines \(\overset{̄}{r}\times \overset{̄}{a} = \overset{̄}{b}\times \overset{̄}{a}\) and \(\overset{̄}{r}\times \overset{̄}{b} = \overset{̄}{a}\times \overset{̄}{b}\) is

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

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 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:

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...