Question

Obtain the Expression for rectangular components of a given vector A in x-y plane

Answer 1

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Answer 2

The rectangular components of a given vector A in x-y plane is $\vec{A_{1}}$ and $\vec{A_{2}}$

Explanation:  

According to diagram,

$\vec{A_{1}}$ and $\vec{A_{2}}$ are components of $\vec{A}$

According to new diagram,

$\vec{A}=\vec{A_{x}}+\vec{A_{y}}$

$\vec{A}=\vec{A_{x}}\hat{i}+\vec{A_{y}}\hat{j}$

$\sin\theta=\dfrac{QR}{OQ}$

Put the value into the formula

$\sin\theta=\dfrac{\vec{A_{y}}}{\vec{A}}$

$A_{y}=A\sin\theta$....(I)

$A_{x}=A\cos\theta$.....(II)

Divided equation (I) by (II)

$\dfrac{A_{y}}{A_{x}}=\tan\theta$

$\tan\theta=\dfrac{A_{y}}{A_{x}}$

Hence, The rectangular components of a given vector A in x-y plane is $\vec{A_{1}}$ and $\vec{A_{2}}$

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Topic : rectanguklar component

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