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 $^{\circ}$)

With respect to a rectangular cartesian coordinate system,three vectors are expressed as $\vec a = 4\hat i - \hat j$,$\vec b = -3\hat i + 2\hat j$,and $\vec c = -\hat k$,where $\hat i, \hat j, \hat k$ are unit vectors along the $X, Y,$ and $Z$-axis respectively. The unit vector $\hat r$ along the direction of the sum of these vectors is:

Three vectors each of magnitude $3 \sqrt{1.5}$ units are acting at a point. If the angle between any two vectors is $\frac{\pi}{3}$,then the magnitude of the resultant vector of the three vectors is

$A$ truck travelling due north at $20 \, m/s$ turns west and travels at the same speed. The change in its velocity is

The unit vector parallel to the resultant of vectors $\vec{A} = 4\hat{i} - 3\hat{j}$ and $\vec{B} = 8\hat{i} + 8\hat{j}$ is:

Given that $P + Q + R = 0$. Which of the following statements is true?