A vector has magnitude same as that of $\overrightarrow{\mathrm{A}}-=3 \hat{\mathrm{j}}+4 \hat{\mathrm{j}}$ and is parallel to $\overrightarrow{\mathrm{B}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$. The $\mathrm{x}$ and $y$ components of this vector in first quadrant are $\mathrm{x}$ and $3$ respectively where  $X$=_____.

Let $\overrightarrow A = \hat iA\,\cos \theta + \hat jA\,\sin \theta $ be any vector. Another vector $\overrightarrow B $ which is normal to $\overrightarrow A$ is

The components of $\vec a = 2\hat i + 3\hat j$ along the direction of vector $\left( {\hat i + \hat j} \right)$ is

Let $\vec A\, = \,(\hat i\, + \,\hat j)\,$  and $\vec B\, = \,(2\hat i\, - \,\hat j)\,.$  The magnitude of a coplanar vector $\vec C$ such that  $\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B$ is given by

The area of the parallelogram represented by the vectors $\overrightarrow A = 2\hat i + 3\hat j$ and $\overrightarrow B = \hat i + 4\hat j$ is.......$units$