The resultant of two vectors $\overrightarrow P $ and $\overrightarrow Q $ is $\overrightarrow R .$ If $Q$ is doubled, the new resultant is perpendicular to $P$. Then $R $ equals
$P$
$(P+Q)$
$Q$
$(P-Q)$
The magnitude of a given vector with end points $ (4, -4, 0)$ and $(-2, -2, 0)$ must be
Two vectors $P = 2\hat i + b\hat j + 2\hat k$ and $Q = \hat i + \hat j + \hat k$ will be parallel if $b=$ ........
A particle has displacement of $12 \,m$ towards east and $5 \,m$ towards north then $6 \,m $ vertically upward. The sum of these displacements is........$m$
The magnitude of vector $\overrightarrow A ,\,\overrightarrow B $ and $\overrightarrow C $ are respectively $12, 5$ and $13$ units and $\overrightarrow A + \overrightarrow B = \overrightarrow C $ then the angle between $\overrightarrow A $ and $\overrightarrow B $ is
Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta $ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta $ is ....... $^o$