Question

If `|bara| = |barb|` = 1 and `|bara + barb| = sqrt(3)`, then the value of `(3bara - 4barb)*(2bara + 5barb)` = ______.

Options

• – 2

• `-21/2`

• 21

• `21/2`

Answer 1

If `|bara| = |barb|` = 1 and `|bara + barb| = sqrt(3)`, then the value of `(3bara - 4barb)*(2bara + 5barb)` = `underlinebb(-21/2)`.

Explanation:

`|bara + barb|^2 = |bara|^2 + |barb|^2 + 2bara * barb`

3 = `1 + 1 + 2bara * barb` 

∴ `bara * barb = 1/2`

∴ `(3bara - 4barb)*(2bara + 5barb) = 6a^2 + 7bara * barb - 20b^2`

= `6 + 7/2 - 20`

= `-21/2`