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

Check whether the following vectors are orthogonal. (i) vecA=2hati+3h

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