AP EAPCET 2024 - 21th May Morning Shift | Three Dimensional Geometry Question 21 | Mathematics

Let $\pi$ be the plane that passes through the point $(-2,1,-1)$ and parallel to the plane $2 x-y+2 z=0$. Then the foot of perpendicular drawn from the point $(1,2,1)$ to the plane $\pi$ is

$(-3,-1,1)$

$(-1,1,-3)$

$(-3,3,-1)$

$(-1,3,-1)$

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

The angle between the line with the direction ratios $(2,5,1)$ and the plane $8 x+2 y-z=14$ is

$\cos ^{-1}\left(\frac{64}{\sqrt{9804}}\right)$

$\sin ^{-1}\left(\frac{64}{\sqrt{9804}}\right)$

$\sin ^{-1}\left(\frac{25}{\sqrt{2070}}\right)$

$\cos ^{-1}\left(\frac{25}{\sqrt{2070}}\right)$

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

The direction cosines of the line of intersection of the planes $x+2 y+z-4=0$ and $2 x-y+z-3=0$ are

$\left(\frac{3}{\sqrt{26}}, \frac{1}{\sqrt{26}}, \frac{-4}{\sqrt{26}}\right)$

$\left(\frac{3}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{-1}{\sqrt{14}}\right)$

$\left(\frac{3}{\sqrt{35}}, \frac{1}{\sqrt{35}}, \frac{-5}{\sqrt{35}}\right)$

$\left(\frac{3}{\sqrt{22}}, \frac{-2}{\sqrt{22}}, \frac{3}{\sqrt{22}}\right)$

AP EAPCET 2024 - 20th May Evening Shift

MCQ (Single Correct Answer)

-0

If $L_1$ and $L_2$ are two lines which pass through origin and having direction ratios $(3,1,-5)$ and $(2,3,-1)$ respectively, then equation of the plane containing $L_1$ and $L_2$ is

$4 x+5 y-63=0$

$5 x-y+3 z=0$

$2 x-y+z=0$

$x-5 y+3 z=0$

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