QRS is a triangle such that \(\overrightarrow{QR} = (3i + 2j)\) and \(\overrightarrow{SR} = (-5i + 3j)\), find \(\overrightarrow{SQ}\).

QRS is a triangle such that \(\overrightarrow{QR} = (3i + 2j)\) and \(\overrightarrow{SR} = (-5i + 3j)\), find \(\overrightarrow{SQ}\).

Answer Details

To find \(\overrightarrow{SQ}\), we can use the fact that \(\overrightarrow{SR} = \overrightarrow{SQ} + \overrightarrow{QR}\). Rearranging this equation to solve for \(\overrightarrow{SQ}\) gives us: $$\overrightarrow{SQ} = \overrightarrow{SR} - \overrightarrow{QR} = (-5i + 3j) - (3i + 2j) = -8i + j$$ Therefore, the value of \(\overrightarrow{SQ}\) is -8i + j. So, the correct option is (A) 8i + j.