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प्रश्न
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`.
उत्तर
`vec"v"_1 + vec"v"_2 = (2hat"i" - 3hat"j") + (-6hat"i" + 5hat"j")`
`= (2hat"i" - 6hat"i") + (-3hat"j" + 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 `vec"R"` with X – axis,
∴ θ = `tan^-1("R"_"y"/"R"_"x")`
`= tan^-1 (2/-4)`
`= tan^-1 (- 1/2)` with X-axis
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