3D Geometry

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JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 11

Let $L$ be the line of intersection of planes $\vec{r}\cdot\left(\hat{i}-\hat{j}+2\hat{k}\right)=2$ and $\vec{r}\cdot\left(2\hat{i}+\hat{j}-\hat{k}\right)=2$. If $P(\alpha,\beta,\gamma)$ is the foot of perpendicular on $L$ from the point $(1,2,0)$, then the value of $35(\alpha+\beta+\gamma)$ is equal to :

3D Geometry

$101$$119$$134$$143$

JEE Main 2021 (Online) 24th February Evening ShiftQuestion 12

Let $a,b\in\mathbf{R}$. If the mirror image of the point $P(a,6,9)$ with respect to the line $\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}$ is $(20,b,-a-9)$, then $|a+b|$ is equal to :

3D Geometry

$84$$86$$88$$90$

JEE Main 2023 (Online) 6th April Morning ShiftQuestion 13

If the equation of the plane passing through the line of intersection of the planes $2x-y+z=3$, $4x-3y+5z+9=0$ and parallel to the line $\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}$ is $ax+by+cz+6=0$, then $a+b+c$ is equal to

3D Geometry

$12$$13$$14$$15$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 14

Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l+m-n=0$ and $l^{2}+m^{2}-n^{2}=0$. Then the value of $\sin^{4}\alpha+\cos^{4}\alpha$ is :

3D Geometry

$\frac{5}{8}$$\frac{3}{8}$$\frac{1}{2}$$\frac{3}{4}$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 15

The equation of the line through the point $(0,1,2)$ and perpendicular to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{-2}$ is :

3D Geometry

$\frac{x}{3}=\frac{y-1}{4}=\frac{z-2}{-3}$$\frac{x}{-3}=\frac{y-1}{4}=\frac{z-2}{3}$$\frac{x}{3}=\frac{y-1}{-4}=\frac{z-2}{3}$$\frac{x}{3}=\frac{y-1}{4}=\frac{z-2}{3}$