TG EAPCET 2024 (Online) 9th May Morning Shift | Three Dimensional Geometry Question 16 | Mathematics

The direction cosines of two lines are connected by the relations $l-m+n=0$ and $2 l m-3 m n+n l=0$. If $\theta$ is the angle between these two lines, then $\cos \theta=$

$\frac{1}{4}$

$\frac{1}{\sqrt{19}}$

$\frac{1}{3}$

$\frac{1}{3 \sqrt{2}}$

TG EAPCET 2024 (Online) 9th May Morning Shift

MCQ (Single Correct Answer)

-0

A plane $\pi$ passes through the points $(5,1,2),(3,-4,6)$ and $(7,0,-1)$. If $p$ is the perpendicular distance from the origin to the plane $\pi$ and $l, m$ and $n$ are the direction cosines of a normal to the plane $\pi$, the $|3 l+2 m+5 n|=$

$3 p$

$2 p$

$p$

$\frac{p}{2}$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

If $M$ is the foot of the perpendicular drawn from $P($ -1,2,-1 ) to the plane passing through the point $A(3,-2,1)$ and perpendicular to the vector $4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$, then the length of $P M$ is

$\frac{16}{3}$

$\frac{18}{5}$

$\frac{22}{9}$

$\frac{28}{9}$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

If $A=(1,-1,2), B=(3,4,-2), C=(0,3,2)$ and $D=(3$, $5,6)$, then the angle between the lines $\mathbf{A B}$ and $\mathbf{C D}$ is

$30^{\circ}$

$45^{\circ}$

$60^{\circ}$

$90^{\circ}$

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