Question

The vector in the direction of the vector `hat"i" - 2hat"j" + 2hat"k"` that has magnitude 9 is ______.

Options

• `hat"i" - 2hat"j" + 2hat"k"`

• `(hat"i" - 2hat"j" + 2hat"k")/3`

• `3(hat"i" - 2hat"j" + 2hat"k")`

• `9(hat"i" - 2hat"j" + 2hat"k")`

Answer 1

The vector in the direction of the vector `hat"i" - 2hat"j" + 2hat"k"` that has magnitude 9 is `3(hat"i" - 2hat"j" + 2hat"k")`.

Explanation:

Let `vec"a" = hat"i" - 2hat"j" + 2hat"k"`

Unit vector in the direction of `vec"a" = vec"a"/|vec"a"|`

= `(hat"i" - 2hat"j" + 2hat"k")/sqrt((1)^2 + (-2)^2 + (2)^2)`

= `(hat"i" - 2hat"j" + 2hat"k")/sqrt(1 + 4 + 4)`

= `(hat"i" - 2hat"j" + 2hat"k")/3`

∴ Vector of magnitude 9 = `(9(hat"i" - 2hat"j" + 2hat"k"))/3`

= `(3hat"i" - 2hat"j" + 2hat"k")`