If vectors ` vec aa n d vec b` are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to `a` is a.` vec b+( vec bxx vec a)/(| vec a|^2)` b. `( vec adot vec b)/(| vec b|^2)` c. ` vec b-( vec bdot vec a)/(| vec a|^2)` d. `( vec axx( vec bxx vec a))/(| vec b|^2)`

Options

A. `vecb+(vecbxxveca)/(|veca|^(2))`
B. `(veca.vecb)/(|vecb|^(2))`
C. `vecb-(vecb.veca)/(|veca|^(2))veca`
D. `(vecaxx(vecbxxveca))/(|vecb|^(2))`

Answer

a

Explanation

`Let , vec(OD) = tveca`
` vec(DB) = vecb - vecta`
`or (vecb -tveca) .veca= 0`
`or t = (vecb.veca)/(|veca|^(2))`
`vec(DB) = vecb- ((vecb.veca)veca)/(|veca|^(2))`