AP EAPCET 2024 - 21th May Morning Shift | Three Dimensional Geometry Question 3 | Mathematics

If $P(2, \beta, \alpha)$ lies on the plane $x+2 y-z-2=0$ and $Q(\alpha,-1, \beta)$ lies on the plane $2 x-y+3 z+6=0$, then the direction cosines of the $P Q$ are

$\left(-\frac{4}{\sqrt{17}}, 0, \frac{1}{\sqrt{17}}\right)$

$\left(+\frac{4}{\sqrt{17}}, 0, \frac{1}{\sqrt{17}}\right)$

$\left(\frac{1}{\sqrt{17}}, 0, \frac{4}{\sqrt{17}}\right)$

$\left(-\frac{1}{\sqrt{17}}, 0, \frac{4}{\sqrt{17}}\right)$

AP EAPCET 2024 - 21th May Morning Shift

MCQ (Single Correct Answer)

-0

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

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

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

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

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

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