Check whether the following vectors are orthogonal.
(i) `vecA=2hati+3hatjandvecB=4hati-5hatj` (ii) `vecC=5hati+2hatjandvecD=2hati+5hatj`

Explanation

`vecA.vecB=8-15=-17ne0`
Hence `vecAandvecB` are not orthogonal to each other.
`vecC.vecD=10-10=0`
Hence. `vecCandvecD` are orthogonal to cach other.
t is also possible to geometrically show that the vectors C and D are orthogonal to each other. This is shown in the following figur.

In physics, the work done by a force `vecF` to move an object through a small displacement di is defined as,
`W=vecF.dvecr`
`W=vecFdrcostheta`
The work done is basically a scalar product between the force vector and the displacement vector. Apart from work done, there are other physical quantities which are also defined through scalar products.