The magnitude of a given vector with end points $ (4, -4, 0)$ and $(-2, -2, 0)$ must be

Two vectors having equal magnitudes of $x\, units$ acting at an angle of $45^o$ have resultant $\sqrt {\left( {2 + \sqrt 2 } \right)} $ $units$. The value of $x$ is

The vectors $5i + 8j$ and $2i + 7j$ are added. The magnitude of the sum of these vector is

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

Give the names of two methods for vector addition. Write the law of parallogram for vector addition.

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is ........ $^o$