$A$ 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?

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

If $\overrightarrow A = 2\hat i + 4\hat j - 5\hat k$,the direction cosines of the vector $\overrightarrow A$ are:

The condition $( a \cdot b )^2 = a^2 b^2$ is satisfied when

In a regular octagon $ABCDEFGH$ with center $O$,what is the sum of $\overrightarrow{ AB }+\overrightarrow{ AC }+\overrightarrow{ AD }+\overrightarrow{ AE }+\overrightarrow{ AF }+\overrightarrow{ AG }+\overrightarrow{ AH }$ if $\overrightarrow{ AO }=2 \hat{ i }+3 \hat{ j }-4 \hat{ k }$?

Given $a+b+c+d=0,$ which of the following statements are correct:
$(a)$ $a, b, c,$ and $d$ must each be a null vector.
$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$.
$(c)$ The magnitude of $a$ can never be greater than the sum of the magnitudes of $b, c,$ and $d$.
$(d)$ $(b+c)$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear,and in the line of $a$ and $d$ if they are collinear.