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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")`
Solution
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")`
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