The horizontal component of vector 'a' is equal to the vertical component of vector 'b'. If 30 degree is the angle made  'a' by with its horizontal axis and that made by 'b' with its vertical axis , then calculate the value of 'b' in terms of 'a'?  

Dear Student,

Please find below the solution to the asked query:

Let the two vectors as $\overrightarrow{a } \& \overrightarrow{b }$.
According to the given information vector $\overrightarrow{a }$ makes an angle 30⁰ with horizontal & vector $\overrightarrow{b }$ makes an angle 60⁰.
It is also mentioned that, the horizontal component of first vector is equal to the vertical component of second vector. Then,

$$\begin{gathered} a \cos {30}^0=b \sin {60}^0 \Rightarrow a\times \left(\frac{\sqrt{3}}{2}\right)=b\times \left(\frac{\sqrt{3}}{2}\right) \\ \Rightarrow \left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right| \end{gathered}$$

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