If vectors $P, Q$ and $R$ have magnitude $5, 12$ and $13 $ units and $\overrightarrow P + \overrightarrow Q = \overrightarrow R ,$ the angle between $Q$ and $R$ is
${\cos ^{ - 1}}\frac{5}{{12}}$
${\cos ^{ - 1}}\frac{5}{{13}}$
${\cos ^{ - 1}}\frac{{12}}{{13}}$
${\cos ^{ - 1}}\frac{7}{{13}}$
Explain commutative law for vector addition.
The position vectors of points $A, B, C$ and $D$ are $\vec A = 3\hat i + 4\hat j + 5\hat k,\,\vec B = 4\hat i + 5\hat j + 6\hat k,\,\vec C = 7\hat i + 9\hat j + 3\hat k$ and $\vec D = 4\hat i + 6\hat j$ then the displacement vectors $\overrightarrow {AB} $ and $\overrightarrow {CD} $ are
Two forces are such that the sum of their magnitudes is $18\; N$ and their resultant is $12\; N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are