Question

Vector of magnitude 3 making equal angles with x and y Perpendicular to z axis is ______.

Options

• `hati+2sqrt2hatj`

• `3hatk`

• `(3sqrt2)/2hati+(3sqrt2)/2hatj`

• `sqrt3hati+sqrt3hatj+sqrt3hatk`

Answer 1

Vector of magnitude 3 making equal angles with x and y Perpendicular to z axis is `bbunderline((3sqrt2)/2hati+(3sqrt2)/2hatj)`.

Explanation:

\[\ce{\overset{->}{{ν}}}\] = `sqrta^2+a^2+0^2=3`

`sqrt2a^2=3`

`asqrt2=3`

⇒ a = ± `3/sqrt2`

\[\ce{\overset{->}{{ν}}}\] = `±3/sqrt2hati±3/sqrt2hatj`

\[\ce{\overset{->}{{ν}}}\] = `±3/sqrt2(hati+hatj)`