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The ratio of maxium and minimum magnitudes of the resultant of two vectors $\left | \vec{a} \right |$ and $\left | \vec{b} \right |$ is 3:1, Now $\left | \vec{a} \right |=$
Option: 1
$\left | \vec{b} \right |$

Option: 2
$2\left | \vec{b} \right |$

Option: 3
$3\left | \vec{b} \right |$

Option: 4
$4\left | \vec{b} \right |$

Answers (1)

best_answer

as we learned

Triangle law of vector Addition -

If two vector are represented by both magnitude and direction by two sides of triangle taken in same order then their resultant is represented by 3^rd side of triangle.

- wherein

Represents triangle law of vector Addition

$\left | \vec{a}+\vec{b} \right |=\sqrt{a^2+b^2+2ab\cos\theta}$

$\left | \vec{a}+\vec{b} \right |_{max}=a+b$ when $\theta=0\degree$

$\left | \vec{a}+\vec{b} \right |_{min}=a-b$ when $\theta=180\degree$

here

$\frac{a+b}{a-b}=\frac{3}{1}$

or

$a+b=3a-3b$

or $2a=4b \: \Rightarrow a=2b$

$\left | \vec{a} \right |=2\left | \vec{b} \right |$

Posted by

manish painkra

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