Question:
The length of longer diagonal of the parallelogram constructed on \( 5a + 2b \) and \( a - 3b \), if it is given that \( |a| = 2\sqrt{2} \), \( |b| = 3 \), and the angle between \( a \) and \( b \) is \( \frac{\pi}{4} \), is?
The length of longer diagonal of the parallelogram constructed on \( 5a + 2b \) and \( a - 3b \), if it is given that \( |a| = 2\sqrt{2} \), \( |b| = 3 \), and the angle between \( a \) and \( b \) is \( \frac{\pi}{4} \), is?
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To find the length of the diagonal in a parallelogram, use the formula involving the squares of the sides and the cosine of the angle between them.
Updated On: Jan 12, 2026
- \( \sqrt{593} \)
- \( \sqrt{113} \)
- \( \sqrt{369} \)
- \( \sqrt{563} \)
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The Correct Option is C
Solution and Explanation
The length of the diagonal of a parallelogram is given by the formula \( \sqrt{(5a + 2b)^2 + (a - 3b)^2} \). By substituting the values of \( a \), \( b \), and the angle, the length of the diagonal is calculated as \( \sqrt{369} \).
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