3D Geometry

Showing 366-370 of 461 questions.

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JEE Main 2026 (Online) 5th April Morning ShiftQuestion 366

The square of the distance of the point of intersection of the lines $\vec r=(\hat i+\hat j-\hat k)+\lambda(a\hat i-\hat j)$, $a\neq0$ and $\vec r=(4\hat i-\hat k)+\mu(2\hat i+a\hat k)$ from the origin is :

3D Geometry

$5$$10$$17$$26$

JEE Main 2026 (Online) 2nd April Morning ShiftQuestion 367

If the point of intersection of the lines $\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}$ and $\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}$ lies on $xy$-plane, then the value of $a+b$ is :

3D Geometry

$2$$5$$7$$9$

JEE Main 2026 (Online) 2nd April Morning ShiftQuestion 368

Let a line $L$ passing through the point $(1,1,1)$ be perpendicular to both the vectors $2\hat i+2\hat j+\hat k$ and $\hat i+2\hat j+2\hat k$. If $P(a,b,c)$ is the foot of perpendicular from the origin on the line $L$, then the value of $34(a+b+c)$ is :

3D Geometry

$50$$80$$100$$120$

JEE Main 2026 (Online) 22nd January Evening ShiftQuestion 369

Let $L$ be the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+3}{6}$ and let $S$ be the set of all points $(a,b,c)$ on $L$, whose distance from the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z-9}{0}$ along the line $L$ is $7$. Then $\sum_{(a,b,c)\in S}(a+b+c)$ is equal to :

3D Geometry

$40$$28$$34$$6$

JEE Main 2026 (Online) 22nd January Morning ShiftQuestion 370

If the image of the point $P(1,2,a)$ in the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{7-z}{2}$ is $Q(5,b,c)$, then $a^2+b^2+c^2$ is equal to :

3D Geometry

$264$$293$$298$$283$