Resolved part of vector `veca` and along vector `vecb " is " veca1` and that prependicular to `vecb " is " veca2` then `veca1 xx veca2` is equl to

Options

A. `((vecaxxvecb).vecb)/(|vecb|^(2))`
B. `((veca.vecb)veca)/(|veca|^(2))`
C. `((veca.vecb)(vecbxxveca))/(|vecb|^(2))`
D. `((veca.vecb)(vecbxxveca))/(|vecbxxveca|)`

Answer

c

Explanation

`veca_(1) = (veca.hatb) hatb = (( veca.vecb)vecb)/(|vecb|^(2))`
` Rightarrow veca_(2) = veca -veca_(1) = veca - ((veca. Vecb)vecb)/(|vecb|^(2))`
Thus ` veca_(1) xx veca_(2) = ((veca.vecb)vecb)/(|vecb|^(2) xx )(veca - ((veca.vecb)vecb)/(|vecb|^(2)))`
` ((veca. vecb)(vecb xx veca))/(|vecb|^(2))`