The length of longer diagonal of the parallelogram constructed on `5a + 2b` and `a-3b` . If it is given that `|a| = 2sqrt(2),|b|` = 3 and angle between a and b is `(pi)/(4)` is

Options

A. 15
B. `sqrt(113)`
C. `sqrt(593)`
D. `sqrt(369)`

Answer

C

Explanation

Given that, `|a| = 2sqrt(2) and |b| = 3`
The longer vector is `5a + 2b + a-3b = 6a - b` length of one diagonal ` = |6a-b|`
`= sqrt(36a^(2) + b^(2) - 2 xx 6|a||b| cos 45^(@))`
` = sqrt(36 xx 8 + 9 - 12 xx 2sqrt(2) xx 3 xx(1)/(sqrt(2)))`
`=sqrt(288+9-12 xx 6) = sqrt(225) = 15`
Other diagonal is `4a + 5b`
It's lenght `= sqrt(16xx8+25xx9+40xx6)`
`= sqrt(593)`