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Question
Answer the following question.
If `vec"v"_1 = 3hat"i" + 4hat"j" + hat"k" and vec"v"_2 = hat"i" - hat"j" - hat"k"`, determine the magnitude of `vec"v"_1 + vec"v"_2`.
Solution
`vec"v"_1 + vec"v"_2 = (3hat"i" + 4hat"j" + hat"k") + (hat"i" - hat"j" - hat"k")`
`= 3hat"i" + hat"i" + 4hat"j" - hat"j" + hat"k" - hat"k"`
`= 4hat"i" + 3hat"j"`
∴ Magnitude of `(vec"v"_1 + vec"v"_2),`
`|vec"v"_1 + vec"v"_2| = sqrt(4^2 + 3^2) = sqrt25` = 5 units
Magnitude of `vec"v"_1 + vec"v"_2` is 5 units.
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