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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.
MHT CET - 2026
MHT CET
Mathematics
Equation of a Line in Space
Identify the co-ordinates of the point where the line joining \( (1,1,1) \) and \( (2,2,2) \) intersects the plane \( x+y+z=9 \).
MHT CET - 2026
MHT CET
Mathematics
Equation of a Line in Space
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
MHT CET - 2025
MHT CET
Mathematics
Equation of a Line in Space
The number of solutions of \(16^{\sin^2 x} + 16^{\cos^2 x} = 10\) in \(0 \le x \le 2\pi\) are
MHT CET - 2025
MHT CET
Mathematics
Equation of a Line in Space
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
MHT CET - 2025
MHT CET
Mathematics
Equation of a Line in Space
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
MHT CET - 2025
MHT CET
Mathematics
Equation of a Line in Space
If the Cartesian equation of a line is $6x-2=3y+1=2z-2$, then the vector equation of the line is
MHT CET - 2023
MHT CET
Mathematics
Equation of a Line in Space
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
MHT CET - 2023
MHT CET
Mathematics
Equation of a Line in Space
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
MHT CET - 2021
MHT CET
Mathematics
Equation of a Line in Space
The vector equation of the line whose Cartesian equations are $y = 2$ and $4x - 3z + 5 = 0$ is
MHT CET - 2021
MHT CET
Mathematics
Equation of a Line in Space
The Cartesian equation of the line passing through the points A(2, 2, 1) and B(1, 3, 0) is
MHT CET - 2021
MHT CET
Mathematics
Equation of a Line in Space