Question

The unit vector perpendicular to the vectors `hati - hatj and hati + hatj` is ______.

पर्याय

• `hatk`

• `-hatk + hatj`

• `(hati - hatj)/sqrt2`

• `(hati + hatj)/sqrt2`

Answer 1

The unit vector perpendicular to the vectors `hati - hatj and hati + hatj` is `bbunderline(hatk)`.

Explanation:

Vector perpendicular to `veca and vecb  "is"  vecc = veca xx vecb`

`vecc = (hati - hatj) xx (hati + hatj)`

= `|(hati, hatj, hatk),(1, -1, 0), (1, 1, 0)|`

= `hati(0) - hatj(0) + hatk(1 + 1)`

= `2hatk`

`"Unit vector"  hatc = vecc/|vecc| = (2hatk)/|2hatk|`

= `(2hatk)/2`

= `hatk`