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Vector & 3D

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE-MAIN 2020
Let $a, b c \in R$ be such that $a^2+b^2+c^2=1$. If $a \cos \theta=b \cos \left(\theta+\frac{2 \pi}{3}\right)=c \cos \left(\theta+\frac{4 \pi}{3}\right)$, where $\theta=\frac{\pi}{9}$, then the angle...
JEE Main Mathematics Easy
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Q JEE MAIN 2019
Let P be the plane, which contains the line of intersection of the planes, x + y + z – 6 = 0 and 2x...
JEE Main Mathematics Medium
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Q JEE MAIN 2019
If a unit vector $\vec{a}$ makes angles $\frac{\pi}{3}$ with $\hat{i}, \frac{\pi}{4}$ with $\hat{j}$ and $\theta \in(0, \pi)$ with $\hat{k}$, then a value of $\theta$ is...
JEE Main Mathematics Easy
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Q JEE MAIN 2019
The vertices $B$ and $C$ of a $\triangle A B C$ lie on the line, $\frac{x+2}{3}=\frac{y-1}{0}=\frac{z}{4}$ such that $B C=5$ units. Then the area (in...
JEE Main Mathematics Hard
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Q JEE Main 2021
Suppose the line $\frac{x-2}{\alpha}=\frac{y-2}{-5}=\frac{z+2}{2}$ lies on the plane $x+3 y-2 z+\beta=0$. Then $(\alpha+\beta)$ is equal to $\_\_\_\_$。
JEE Main Mathematics Easy
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Q JEE MAIN 2021
The square of the distance of the point of intersection of the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+1}{6}$ and the plane $2 x-y+z=6$ from the point $(-1,-1,2)$ is $\_\_\_\_$...
JEE Main Mathematics Easy
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Q JEE MAIN 2020
A vector $\vec{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}(\alpha, \beta \in R)$ lies in the plane of the vectors, $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\hat{i}-\hat{j}+4 \hat{k}$. If $\vec{a}$ bisects the angle...
JEE Main Mathematics Hard
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Q JEE MAIN 2020
Let P be a plane through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1,...
JEE Main Mathematics Easy
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Q JEE MAIN 2019
On which of the following lines lies the point of intersection of the line, $\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}$ and the plane, $x+ y+z=2 ?$
JEE Main Mathematics Easy
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Q JEE MAIN 2019
The plane which bisects the line segment joining the points (–3, –3, 4) and (3, 7, 6) at right angles, passes through which one of...
JEE Main Mathematics Easy
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