What is the product of two vectors if they are parallel or antiparallel?

What happens to the direction and magnitude of a vector when it is multiplied by a positive and a negative scalar $\lambda$?

If vectors $\overrightarrow {A} = \cos\omega t\hat i + \sin\omega t\hat j$ and $\overrightarrow {B} = \cos\frac{\omega t}{2}\hat i + \sin\frac{\omega t}{2}\hat j$ are functions of time,then the value of $t$ at which they are orthogonal to each other is:

What is the angle between $(\overrightarrow P + \overrightarrow Q)$ and $(\overrightarrow P \times \overrightarrow Q)$?

If $\overrightarrow {A} = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow {B} = - \hat i + 3\hat j + 4\hat k$,a unit vector perpendicular to both $\overrightarrow {A}$ and $\overrightarrow {B}$ will be

If vectors $\vec{A} = (2, -3, 1)$ and $\vec{B} = (3, 4, n)$ are perpendicular to each other,find the value of $n$.