Question

Let `bara, barb and barc` be non-zero vectors such that `(bara xx barb) xx barc = 1/3 |barb||barc|bara`. If θ is the acute angle between the vectors `barb and barc`, then sinθ equals

Options

• `(2sqrt2)/3`

• `sqrt2/3`

• `2/3`

• `1/3`

Answer 1

`bb((2sqrt2)/3)`

Explanation:

Given that `(bara xx barb) xx barc = 1/3 |barb||barc|bara`

Clearly `bara and barb` are non collinear

= `(bara.barc)barb - (barb.barc)bara = 1/3|barb|barc|bara|`

Comparing both side.

∴ `bara.barc = 0  "and"-barb.barc = 1/3|barb||barc|`

∴ `cos theta = (-1)/3`

∴ `sin theta = sqrt(1- 1/9) = (2sqrt2)/3`