Can the resultant of three vectors of unequal magnitudes be a zero vector?

$A$ 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?

For the resultant of two vectors $A$ and $B$ to be maximum,the angle between them should be (in $^{\circ}$)

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane,and another vector $\overrightarrow{C}$ lies outside this plane. Then,the resultant of these three vectors,i.e.,$\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$:

If a vector $\overrightarrow{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $

The direction cosines of the vector $\hat{i} + \hat{j} + \sqrt{2}\hat{k}$ are: