JEE Mathematics / Practice

3D Geometry

Showing 186-190 of 461 questions.

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JEE Main 2021 (Online) 27th July Morning ShiftQuestion 186

Let a plane $P$ pass through the point $(3,7,-7)$ and contain the line $\frac{x-2}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$. If distance of the plane $P$ from the origin is $d$, then $d^2$ is equal to ________.

3D Geometry

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JEE Main 2022 (Online) 26th July Evening ShiftQuestion 187

The plane passing through the line $L:lx-y+3(1-l)z=1$, $x+2y-z=2$ and perpendicular to the plane $3x+2y+z=6$ is $3x-8y+7z=4$. If $\theta$ is the acute angle between the line $L$ and the $y$-axis, then $415\cos^2\theta$ is equal to ________.

3D Geometry

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JEE Main 2021 (Online) 31st August Evening ShiftQuestion 188

Suppose the line $\frac{x-2}{\alpha}=\frac{y-2}{-5}=\frac{z+2}{2}$ lies on the plane $x+3y-2z+\beta=0$. Then $(\alpha+\beta)$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2021 (Online) 26th August Morning ShiftQuestion 189

Let the line $L$ be the projection of the line $\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-4}{2}$ in the plane $x-2y-z=3$. If $d$ is the distance of the point $(0,0,6)$ from $L$, then $d^{2}$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2022 (Online) 29th July Morning ShiftQuestion 190

Let a line with direction ratios $a,-4a,-7$ be perpendicular to the lines with direction ratios $3,-1,2b$ and $b,a,-2$. If the point of intersection of the line $\frac{x+1}{a^2+b^2}=\frac{y-2}{a^2-b^2}=\frac z1$ and the plane $x-y+z=0$ is $(\alpha,\beta,\gamma)$, then $\alpha+\beta+\gamma$ is equal to ________.

3D Geometry

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