Question

Compute the magnitude of the following vector:

`veca = hati + hatj + hatk;` `vecb = 2hati - 7hatj - 3hatk`;  `vecc = 1/sqrt3 hati + 1/sqrt3 hatj - 1/sqrt3 hatk`

Answer 1

The given vectors are:

`veca = hati + hatj + hatk;  vecb = 2hati - 7hatj - 3hatk;  vecc = 1/sqrt3hati + 1/sqrt3hatj - 1/sqrt3hatk`

`|a| = sqrt((1)^2 + (1)^2 + (1)^2) = sqrt3`

`|b| = sqrt((2)^2 + (-7)^2 + (-3)^2)`

= `sqrt(4 + 49 + 9)`

= `sqrt62`

We have, `vecc = 1/sqrt3hati + 1/sqrt3 hatj - 1/sqrt3 hatk`

∴ `|vecc| = sqrt((1/sqrt2)^2 + (1/sqrt3)^2 + (-1/sqrt3)^2`

`= sqrt (1/3 + 1/3 + 1/3)`

`= sqrt(3/3)`

 `= sqrt1`

= 1