Given $A = \hat{i} + \hat{j} + \hat{k}$ and $B = -\hat{i} - \hat{j} - \hat{k}$,then the angle between $(A - B)$ and $A$ is: (in $^{\circ}$)

Let $\vec{P} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{Q} = -(\hat{i} + \hat{j} + \hat{k})$. The angle between $(\vec{P} - \vec{Q})$ and $\vec{P}$ is (in $^\circ$)

Explain the triangle method (head-to-tail method) of vector addition.

If the magnitude of the resultant of two vectors of equal magnitude is equal to the magnitude of either vector,then find the angle between the two vectors. (in $^{\circ}$)

$A$ vector $\vec Q$ which has a magnitude of $8$ is added to the vector $\vec P$ which lies along the $x$-axis. The resultant of the two vectors lies along the $y$-axis and has a magnitude twice that of $\vec P$. The magnitude of $\vec P$ is:

If $\overrightarrow A = 2\hat i + \hat j$,$\overrightarrow B = 3\hat j - \hat k$,and $\overrightarrow C = 6\hat i - 2\hat k$,then the value of $\overrightarrow A - 2\overrightarrow B + 3\overrightarrow C$ is: