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Standard XII

Mathematics

Addition of Vectors

If the result...

Question

If the resultant of two vectors of magnitude 12 N and 5 N is 13 N, what is the angle between them?

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Solution

We know that,
$R^{2} = A^{2} + B^{2} + 2 A B c o s θ \Rightarrow 13^{2} = 12^{2} + 5^{2} + 2 \times 12 \times 5 \times c o s θ \Rightarrow 169 = 144 + 25 + 120 c o s θ \Rightarrow c o s θ = 0 \Rightarrow θ = 90^{\circ}$

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If the resultant of two vectors of magnitude 12 N and 5 N is 13 N, what is the angle between them?

We know that, R2=A2+B2+2ABcosθ⇒132=122+52+2×12×5×cosθ⇒169=144+25+120cosθ⇒cosθ=0⇒θ=90∘

We know that,
$R^{2} = A^{2} + B^{2} + 2 A B c o s θ \Rightarrow 13^{2} = 12^{2} + 5^{2} + 2 \times 12 \times 5 \times c o s θ \Rightarrow 169 = 144 + 25 + 120 c o s θ \Rightarrow c o s θ = 0 \Rightarrow θ = 90^{\circ}$