AP EAPCET 2024 - 22th May Evening Shift | Three Dimensional Geometry Question 3 | Mathematics

If a line $L$ makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$-axis and $Z$-axis respectively, then the angle between $L$ and another line having direction ratio $1,1,1$ is

$\cos ^{-1}\left(\frac{2}{\sqrt{6}}\right)$

$\cos ^{-1}\left(\frac{\sqrt{2}+1}{3 \sqrt{3}}\right)$

$\cos ^{-1}\left(\frac{\sqrt{2}-1}{3}\right)$

$\cos ^{-1}\left(\frac{\sqrt{2}+1}{\sqrt{6}}\right)$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

If $l, m$ and $n$ are the direction cosines of a line that is perpendicular to the lines having the direction ratios $(1,2,-1)$ and $(1,-2,1)$, then $(l+m+n)^2$ is equal to

$\frac{1}{20}$

$\frac{9}{5}$

$\frac{1}{5}$

$\frac{3}{20}$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

The foot of the perpendicular drawn from a point $A(1,1,1)$ on to a plane $\pi$ is $P(-3,3,5)$.If the equation of the plane parallel to the plane of $\pi$ and passing through the mid-point of $A P$ is $a x-y+c z+d=0$, then $a+c-d$ is equal to

-10

-12

AP EAPCET 2024 - 22th May Morning Shift

MCQ (Single Correct Answer)

-0

The distance of a point $(2,3,-5)$ from the plane $\hat{\mathbf{r}} \cdot(4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})=4$ is

$\frac{11}{2}$

$\frac{11}{\sqrt{29}}$

$\frac{15}{\sqrt{29}}$

$\frac{11}{\sqrt{38}}$

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