Question

If `|bar a|` = 5, `|bar b|` = 13 and `|bara xx barb|` = 25 then `|bar a * bar b|` is equal to ______.

Options

• 30

• 60

• 40

• 45

Answer 1

If `|bar a|` = 5, `|bar b|` = 13 and `|bara xx barb|` = 25 then `|bar a * bar b|` is equal to 60.

Explanation:

We use the identity

`|bara xx barb|^2 + (bara * barb)^2 = |bara|^2|barb|^2`

Given, `|bar a|` = 5, `|bar b|` = 13 and `|bara xx barb|` = 25

Substituting the values,

`25^2 + (bara * barb)^2 = 5^2 xx 13^2`

`625 + (bara * barb)^2 = 25 xx 169`

`625 + (bara * barb)^2 = 4225`

`(bara * barb)^2 = 4225 - 625`

`(bara * barb)^2 = 3600`

`|bara * barb| = sqrt3600`

`|bara * barb| = 60`