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

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?

The value of a unit vector in the direction of vector $\vec A = 5\hat i - 12\hat j$ is:

The resultant magnitude of two vectors of same magnitude is equal to the magnitude of either. The angle between the two vectors is (in $^{\circ}$)

What is the minimum number of non-zero vectors in different planes that can be added to give a zero resultant?

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