Consider a vector \[ p = 2 i + 3 j + 2 k\] in the coordinate system \[ ( i,\, j,\, k ).\] The axes are rotated anti-clockwise about the Y-axis by an angle of 60°. The vector \[ p \] in the rotate coordinate system \[ ( i,\, j,\, k )\] is

Consider a vector $$\overrightarrow{\mathbf{p}}=2\hat{\mathbf{i}}+3\hat{\mathbf{j}}+2\hat{\mathbf{k}}$$     in the coordinate system $$\left(\hat{\mathbf{i}},\hat{\mathbf{j}},\hat{\mathbf{k}}\right).$$   The axes are rotated anti-clockwise about the Y-axis by an angle of 60°. The vector $$\overrightarrow{p}$$ in the rotate coordinate system $$\left(\hat{\mathbf{i}},\hat{\mathbf{j}},\hat{\mathbf{k}}\right)$$   is

Answer: Option A