Q.
The length of longer diagonal of the parallelogram constructed on 5a+2b and a−3b, if it is given that ∣a∣=22,∣b∣=3 and the angle between a and b is 4π, is
Given : ∣a∣=22,∣b∣=3
One diagonal is 5a+2b+a−3b=6a−b
Length of one diagonal =∣6a−b∣ =36a2+b2−2×6∣a∣.∣b∣.cos45∘ =36×8+9−12×22×3×21 =288+9−12×6=225=15
Other diagonal is 4a+5b. Its length is =(4a)2+(5b2)+2×∣4a∣∣5b∣cos45∘ =16×8+25×9+40×6=593