Question

If `vecA` and `vecB` is two vectors satisfying the relation `vecA.vecB = [vecA xx vecB]`. Then the value of `[vecA - vecB]` will be ______.

पर्याय

• `sqrt(A^2 + B^2 - sqrt2 AB)`

• `sqrt(A^2 + B^2)`

• `sqrt(A^2 + B^2 + sqrt2 AB)`

• `sqrt(A^2 - B^2 - sqrt2AB)`

Answer 1

If `vecA` and `vecB` is two vectors satisfying the relation `vecA.vecB = [vecA xx vecB]`. Then the value of `[vecA - vecB]` will be `underlinebb(sqrt(A^2 + B^2 - sqrt2 AB))`.

Explanation:

`vecA.vecB = vecA xx vecB` .........[given]

`|vecA||vecB|costheta = |vecA||vecB|sintheta  hatn`

This is only possible when θ = 45°.

`|vecA - vecB| = sqrt(A^2 + B^2 + 2A(-B)costheta)`

= `sqrt(A^2 + B^2 - 2ABcos45^circ)`

= `sqrt(A^2 + B^2 - sqrt2AB)`