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

Which of the following statement$(s)$ is/are correct?

Establish the following vector inequalities geometrically or otherwise:
$(a) \quad |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}|$
$(b) \quad |\vec{a} + \vec{b}| \geq ||\vec{a}| - |\vec{b}||$
$(c) \quad |\vec{a} - \vec{b}| \leq |\vec{a}| + |\vec{b}|$
$(d) \quad |\vec{a} - \vec{b}| \geq ||\vec{a}| - |\vec{b}||$
When does the equality sign apply in each case?

If two vectors $2\hat{i} + 3\hat{j} - \hat{k}$ and $-4\hat{i} - 6\hat{j} + \lambda\hat{k}$ are parallel to each other,then the value of $\lambda$ is:

The resultant of two vectors $A$ and $B$ makes an angle $\alpha$ with $A$ and $\beta$ with $B$. Which of the following is correct?

The unit vector along $\hat{i} + \hat{j}$ is