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# Answer the following question. For v→1=2i^-3j^andv→2=-6i^+5j^, determine the magnitude and direction of v→1+v→2. - Physics

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

Is there an error in this question or solution?
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#### APPEARS IN

Balbharati Physics 11th Standard Maharashtra State Board
Chapter 2 Mathematical Methods
Exercises | Q 2. (iii) | Page 29
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