Question

For non zero, non collinear vectors `vecp` and `vecq`, the value of `[(hati, vecp, vecq)]hati + [(hatj, vecp, vecq)]hatj + [(hatk, vecp, vecq)]hatk` is ______.

पर्याय

• `vec0`

• `2(vecp xx vecq)`

• `(vecq xx vecp)`

• `(vecp xx vecq)`

Answer 1

For non zero, non collinear vectors `vecp` and `vecq`, the value of `[(hati, vecp, vecq)]hati + [(hatj, vecp, vecq)]hatj + [(hatk, vecp, vecq)]hatk` is `underlinebb((vecp xx vecq))`.

Explanation:

We can write the given expression

= `{hati.(vecp xx vecq)}hati + {hatj.(vecp xx vecq)}hatj + {hatk.(vecp xx vecq)}hatk`

= `vecp xx vecq`

Since for any vector `veca`,

`veca = (veca.hati)hati + (veca.hatj)hatj + (veca.hatk)hatk`