AP EAPCET 2024 - 23th May Morning Shift | Three Dimensional Geometry Question 3 | 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 $\sin \theta=\frac{1}{3^{\prime}}$ then the value of $\lambda=$

$\frac{3}{5}$

$\frac{5}{4}$

$\frac{5}{3}$

$\frac{4}{3}$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

If $A=(1,2,3), B=(3,4,7)$ and $C=(-3,-2,-5)$ are three points, then the ratio in which the point $C$ divides $A B$ externally is

$2: 3$

$3: 2$

$4: 3$

$3: 4$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}$ are the vertices of a tetrahedron, then its volume is

$1 / 6$

$2 / 3$

$1 / 3$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

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

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

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

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

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

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