JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Vector

When the position vector $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$ changes sign as $-\overrightarrow{\mathrm{r}}$, which one of the following vector will not flip under sign change ?

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 $\overrightarrow{\mathrm{B}}=2\hat{\mathrm{i}}-2\hat{\mathrm{j}}+4\mathrm{p}\hat{\mathrm{k}}$, respectively. If both the vec …

Two forces ${\overrightarrow{\mathrm{F}}}_1$ and ${\overrightarrow{\mathrm{F}}}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between …

A particle moves in $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\overrightarrow{\mathrm{P}}(\mathrm{t})=\hat{\mathrm{i}}\cos (\mathrm{kt})-\hat{\mathrm{j}}\sin (\mathrm{kt})$. If k is constant, the angle between …

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

For three vectors $\vec{A}=(-x\hat{i}-6\hat{j}-2\hat{k})$, $\vec{B}=(-\hat{i}+4\hat{j}+3\hat{k})$ and $\vec{C}=(-8\hat{i}-\hat{j}+3\hat{k})$, if $\vec{A}\cdot (\vec{B}\times \vec{C})=0$, then value of x is ______.