JEE Mathematics / Practice

3D Geometry

Showing 196-200 of 461 questions.

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JEE Main 2023 (Online) 10th April Evening ShiftQuestion 196

Let the foot of perpendicular from the point $A(4,3,1)$ on the plane $P:x-y+2z+3=0$ be $N$. If $B(5,\alpha,\beta)$, $\alpha,\beta\in\mathbb{Z}$ is a point on plane $P$ such that the area of the triangle $ABN$ is $3\sqrt{2}$, then $\alpha^{2}+\beta^{2}+\alpha\beta$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2022 (Online) 27th July Morning ShiftQuestion 197

Let the line $\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z-3}{-4}$ intersect the plane containing the lines $\frac{x-4}{1}=\frac{y+1}{-2}=\frac z1$ and $4ax-y+5z-7a=0=2x-5y-z-3$, $a\in\mathbb{R}$ at the point $P(\alpha,\beta,\gamma)$. Then the value of $\alpha+\beta+\gamma$ equals ________.

3D Geometry

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JEE Main 2020 (Online) 3rd September Evening ShiftQuestion 198

Let a plane $P$ contain two lines $\vec r=\hat i+\lambda(\hat i+\hat j)$, $\lambda\in\mathbf{R}$ and $\vec r=-\hat j+\mu(\hat j-\hat k)$, $\mu\in\mathbf{R}$. If $Q(\alpha,\beta,\gamma)$ is the foot of the perpendicular drawn from the point $M(1,0,1)$ to $P$, then $3(\alpha+\beta+\gamma)$ equals ________.

3D Geometry

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JEE Main 2022 (Online) 25th June Evening ShiftQuestion 199

Let $l_1$ be the line in $xy$-plane with $x$ and $y$ intercepts $\frac{1}{8}$ and $\frac{1}{4\sqrt{2}}$ respectively, and $l_2$ be the line in $zx$-plane with $x$ and $z$ intercepts $-\frac{1}{8}$ and $-\frac{1}{6\sqrt{3}}$ respectively. If $d$ is the shortest distance between the line $l_1$ and $l_2$, then $d^{-2}$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2022 (Online) 27th June Morning ShiftQuestion 200

Let the mirror image of the point $(a,b,c)$ with respect to the plane $3x-4y+12z+19=0$ be $(a-6,\beta,\gamma)$. If $a+b+c=5$, then $7\beta-9\gamma$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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