Sum

**Answer the following question.**

For `vec"v"_1 = 2hat"i" - 3hat"j" and vec"v"_2 = -6hat"i" + 5hat"j"`, determine the magnitude and direction of `vec"v"_1 + vec"v"_2`.

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#### Solution

`vec"v"_1 + vec"v"_2 = (2hat"i" - 3hat"j") + (-6hat"i" + 5hat"j")`

`= (2hat"i" - 6hat"j") + (-3hat"i" + 5hat"j")`

`= -4hat"i" + 2hat"j"`

∴ `|vec"v"_1 + vec"v"_2| = sqrt((-4)^2 + 2^2) = sqrt20 = sqrt(4 xx 5) = 2sqrt5`

Comparing `vec"v"_1 + vec"v"_2` with `vec"R" = "R"_"x" hat"i" + "R"_"y" hat"j"`

`=> "R"_"x" = - 4 and "R"_"y" = 2`

Taking θ to be angle made by R `vec"R"` with X – axis,

∴ θ = `tan^-1("R"_"y"/"R"_"x") = tan^-1 (2/-4)`

`= tan^-1 (- 1/2)` with X-axis

Concept: Resolution of Vectors

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