JEE Mathematics / Practice

3D Geometry

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JEE Main 2022 (Online) 28th June Evening ShiftQuestion 176

Let the image of the point $P(1,2,3)$ in the line $L:\frac{x-6}{3}=\frac{y-1}{2}=\frac{z-2}{3}$ be $Q$. Let $R(\alpha,\beta,\gamma)$ be a point that divides internally the line segment $PQ$ in the ratio $1:3$. Then the value of $22(\alpha+\beta+\gamma)$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2023 (Online) 8th April Evening ShiftQuestion 177

Let $P_1$ be the plane $3x-y-7z=11$ and $P_2$ be the plane passing through the points $(2,-1,0)$, $(2,0,-1)$, and $(5,1,1)$. If the foot of the perpendicular drawn from the point $(7,4,-1)$ on the line of intersection of the planes $P_1$ and $P_2$ is $(\alpha,\beta,\gamma)$, then $\alpha+\beta+\gamma$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2023 (Online) 6th April Morning ShiftQuestion 178

Let the image of the point $P(1,2,3)$ in the plane $2x-y+z=9$ be $Q$. If the coordinates of the point $R$ are $(6,10,7)$, then the square of the area of the triangle $PQR$ is $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2022 (Online) 29th June Morning ShiftQuestion 179

Let $P_1:\vec{r}\cdot\left(2\hat{i}+\hat{j}-3\hat{k}\right)=4$ be a plane. Let $P_2$ be another plane which passes through the points $(2,-3,2)$, $(2,-2,-3)$ and $(1,-4,2)$. If the direction ratios of the line of intersection of $P_1$ and $P_2$ be $16,\alpha,\beta$, then the value of $\alpha+\beta$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2022 (Online) 24th June Morning ShiftQuestion 180

Let a line having direction ratios $1,-4,2$ intersect the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{2}=\frac{y-7}{3}=\frac{z}{1}$ at the points $A$ and $B$. Then $(AB)^{2}$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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