Vectors JEE Main PYQs, 2019 to 2025

Two particles are located at equal distance from origin. The position vectors of those are represented by ${\vec{A}}=2{\hat{i}}+3n{\hat{j}}+2{\hat{k}}$ and ${\bar{B}}=2{\hat{i}}-2{\hat{j}}+4p{\hat{k}}$, respectively. If both the vectors are at right angle to each other, the value of $n^{{-1}}$ is ________ .

A force $\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i}-2 \hat{j}-\hat{k}$ What will be the value of $b$, if work done on the particle is zero.

The angle between vector ${\vec{Q}}$ and the resultant of $(2{\vec{Q}}+2{\vec{P}})$ and $(2{\vec{Q}}-2{\vec{P}})$ is :

If $\vec{P}=3{\hat{i}}+\sqrt{3}{\hat{j}}+2{\hat{k}}$ and $\vec{Q}=4{\hat{i}}+\sqrt{3}{\hat{j}}+2.5{\hat{k}}$ then, the unit vector in the direction of $\vec{P}\times \vec{Q}$ is ${\frac{1}{x}}\left({\sqrt{3}{\hat{i}}+{\hat{j}}-2\sqrt{3}{\hat{k}}}\right)$. The value of $x$ is _________.