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Vector & 3D

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|2 \vec{a}+3 \vec{b}|=|3 \vec{a}+\vec{b}|$ and the angle between $\vec{a}$ and $\vec{b}$ is $60^{\circ}$. If $\frac{1}{8} \vec{a}$...
JEE Main Mathematics Easy
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Q JEE Main 2021
The distance of the point $(-1,2,-2)$ from the line of intersection of the planes $2 x+3 y+2 z=0$ and $x-2 y+z =0$ is :
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let the equation of the plane, that passes through the point $(1,4,-3)$ and contains the line of intersection of the planes $3 x-2 y+4 z-7=0$...
JEE Main Mathematics Easy
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Q JEE Main 2021
Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors mutually perpendicular to each other and have same magnitude. If a vector $\vec{r}$ satisfies. $...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Equation of a plane at a distance $\sqrt{\frac{2}{21}}$ from the origin, which contains the line of intersection of the planes $x- y-z-1=0$ and $...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to a line, whose direction...
JEE Main Mathematics Medium
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Q JEE Main 2021
Let the line $L$ be the projection of the line $\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-4}{2}$ in the plane $x-2 y-z=3$. If $d$ is the distance of the point $(0,0,6)$...
JEE Main Mathematics Medium
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Q JEE Main 2021
A plane P contains the line x + 2y + 3z + 1 = 0 = x – y – z – 6, and is...
JEE Main Mathematics Easy
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Q JEE Main 2021
Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{j}-\hat{k}$. If $\vec{c}$ is a vector-such that $\vec{a} \times \vec{c}=\vec{b}$ and $\vec{a} \cdot \vec{c}=3$, then $\vec{a} \cdot(\vec{b} \times \vec{c})$ is equal to:
JEE Main Mathematics Easy
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Q JEE MAIN_2021_
The angle between the straight lines, whose direction cosines are given by the equations $2 \ell+2 \mathrm{~m}-\mathrm{n}=0$ and $\mathrm{mn}+\mathrm{n} \ell+\ell \mathrm{m}=0$, is:
JEE Main Mathematics Easy
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