Given $\vec{P} + \vec{Q} = \vec{P} - \vec{Q}$. Under what condition is this true?

If three vectors along coordinate axes represent the adjacent sides of a cube of length $b$,then the unit vector along its diagonal passing through the origin will be

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to vector $\vec{A}$,and the resultant magnitude is equal to half of the magnitude of $\vec{B}$. Then,the angle between $\vec{A}$ and $\vec{B}$ is: (in $^{\circ}$)

$A$ unit vector is represented as $(0.8 \hat{i} + b \hat{j} + 0.4 \hat{k})$. Hence,the value of $b$ must be:

$A$ particle is moving with speed $6 \, m/s$ along the direction of $\vec{A} = 2\hat{i} + 2\hat{j} - \hat{k}$. What is its velocity vector?

When a particle moves from point $A(2,2,3)$ to point $B(6,6,9)$,its displacement vector is