The sum of the magnitudes of two forces is $25 \,N$. The resultant of these forces is perpendicular to the smaller force and has a magnitude of $10 \,N$. The two forces are:

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

If the direction of a vector $\overrightarrow{A}$ is reversed,find $\Delta \overrightarrow{A}$ and $|\Delta \overrightarrow{A}|$.

The vector sum of the two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence, the forces $\vec{A}$ and $\vec{B}$ are

The resultant of two vectors at an angle $150^{\circ}$ is $10$ units and is perpendicular to one vector. The magnitude of the smaller vector is ....... units

Vectors $\vec{A}$ and $\vec{B}$ make angles of $20^\circ$ and $110^\circ$ with the $X$-axis,respectively. The magnitudes of these vectors are $5 \, m$ and $12 \, m$,respectively. The magnitude of the resultant vector of these two vectors is ....... $m$.