$A$ physical quantity which has a direction:

If a unit vector is represented as $\overrightarrow{u} = 0.4 \hat{i} + 0.7 \hat{j} + c \hat{k}$,then the value of '$c$' is

State whether the following statements are true or false:
$(a)$ The unit vectors ${\hat i}$ and ${\hat j}$ along the $x$ and $y$-axes change with time.
$(b)$ If the angle between $\overrightarrow A$ and $\overrightarrow B$ is ${\theta _1}$ and the angle between $\overrightarrow A$ and $\overrightarrow C$ is ${\theta _2}$,then $\overrightarrow A \cdot \overrightarrow B = \overrightarrow A \cdot \overrightarrow C$ implies $\overrightarrow B = \overrightarrow C$.
$(c)$ The resultant vector of two coplanar vectors is also a coplanar vector.

If $\vec P = \vec Q$,then which of the following is $NOT$ correct?

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

$A$ 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?