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Yukti Vault

JEE Mathematics / Practice

3D Geometry

Chapter overview and full question list

Showing 166-170 of 461 questions.

JEE Main 2023 (Online) 11th April Morning ShiftQuestion 166
Let a line $l$ pass through the origin and be perpendicular to the lines $l_1:\vec{r}=\left(\hat{i}-11\hat{j}-7\hat{k}\right)+\lambda\left(\hat{i}+2\hat{j}+3\hat{k}\right)$, $\lambda\in\mathbb{R}$ and $l_2:\vec{r}=\left(-\hat{i}+\hat{k}\right)+\mu\left(2\hat{i}+2\hat{j}+\hat{k}\right)$, $\mu\in\mathbb{R}$. If $P$ is the point of intersection of $l$ and $l_1$, and $Q(\alpha,\beta,\gamma)$ is the foot of perpendicular from $P$ on $l_2$, then $9(\alpha+\beta+\gamma)$ is equal to $\_\_\_\_\_\_$ .
3D Geometry
JEE Main 2023 (Online) 6th April Evening ShiftQuestion 167
If the lines $\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha}$ and $\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta}$ intersect, then the magnitude of the minimum value of $8\alpha\beta$ is $\_\_\_\_\_\_$ .
3D Geometry
JEE Main 2023 (Online) 8th April Morning ShiftQuestion 168
Let $\lambda_1,\lambda_2$ be the values of $\lambda$ for which the points $\left(\frac{5}{2},1,\lambda\right)$ and $(-2,0,1)$ are at equal distance from the plane $2x+3y-6z+7=0$. If $\lambda_1>\lambda_2$, then the distance of the point $(\lambda_1-\lambda_2,\lambda_2,\lambda_1)$ from the line $\frac{x-5}{1}=\frac{y-1}{2}=\frac{z+7}{2}$ is $\_\_\_\_\_\_$ .
3D Geometry
JEE Main 2024 (Online) 6th April Evening ShiftQuestion 169
If the shortest distance between the lines $\frac{x-\lambda}{3}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $\frac{x+2}{-3}=\frac{y+5}{2}=\frac{z-4}{4}$ is $\frac{44}{\sqrt{30}}$, then the largest possible value of $|\lambda|$ is equal to $\_\_\_\_\_\_$ .
3D Geometry
JEE Main 2024 (Online) 30th January Evening ShiftQuestion 170
Let a line passing through the point $(-1,2,3)$ intersect the lines $L_1:\frac{x-1}{3}=\frac{y-2}{2}=\frac{z+1}{-2}$ at $M(\alpha,\beta,\gamma)$ and $L_2:\frac{x+2}{-3}=\frac{y-2}{-2}=\frac{z-1}{4}$ at $N(a,b,c)$. Then, the value of $\frac{(\alpha+\beta+\gamma)^{2}}{(a+b+c)^{2}}$ equals $\_\_\_\_\_\_$ .
3D Geometry