MHT CET 2025 19th April Morning Shift | Three Dimensional Geometry Question 24 | Mathematics

If the angle $\theta$ between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2 x-y+\sqrt{\lambda} z+4=0$ is such that $\sin \theta=\frac{1}{3}$, then $\lambda+1=$

$\frac{5}{3}$

$\frac{-5}{3}$

$\frac{8}{3}$

$\frac{-8}{3}$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

If the directed line makes an angle $45^{\circ}$ and $60^{\circ}$ with the X and Y -axes respectively, then the obtuse angle $\theta$ made by the line with the Z -axis is

$135^{\circ}$

$120^{\circ}$

$160^{\circ}$

$150^{\circ}$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

The co-ordinates of the foot of the perpendicular from the point $(0,2,3)$ on the line $\frac{x+3}{5}=\frac{y+1}{2}=\frac{z+4}{3}$ is

$\left(\frac{48}{19}, \frac{23}{19}, \frac{-13}{19}\right)$

$\left(\frac{-48}{19}, \frac{23}{19}, \frac{-13}{19}\right)$

$\left(\frac{-48}{19}, \frac{-23}{19}, \frac{-13}{19}\right)$

$\left(\frac{48}{19}, \frac{-23}{19}, \frac{-13}{19}\right)$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

A line having direction ratios $1,-4,2$ intersects the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{2}=\frac{y-7}{3}=\frac{z}{1}$ at the points $A$ and $B$ resp., then co-ordinates of points A and B are

$\mathrm{A}(-8,6,-7)\qquad$ $\mathrm{B}(-6,-2,-3)$

$\mathrm{A}(8,6,7)\qquad$ $\mathrm{B(6,2,3)}$

$\mathrm{A}(8,6,7)\qquad$ $\mathrm{B}(6,-2,-3)$

$\mathrm{A}(7,6,8)\qquad$ $\mathrm{B}(-3,-2,6)$

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