What displacement must be added to the displacement $25\hat i - 6\hat j\,\,m$ to give a displacement of $7.0\, m$ pointing in the $X- $direction

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 ....... $^o$

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

Given $a+b+c+d=0,$ which of the following statements eare correct:

$(a)\;a, b,$ c, and $d$ must each be a null vector,

$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$

$(c)$ The magnitude of a can never be greater than the sum of the magnitudes of $b , c ,$ and $d$

$(d)$ $b + c$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear, and in the line of a and $d ,$ if they are collinear ?

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

For the resultant of the two vectors to be maximum, what must be the angle between them....... $^o$