Question

A vector of magnitude 10 has its rectangular component as as 8 and 6 along x axis and y axis respectively. Find the angles it make with the x and y axis?

• A. ${36.87}^{o}withx-axis,{53.13}^{o}withy-axis$
• B. ${53.14}^{o}withx-axis,{36.86}^o$ with y -axis
• C. ${47.16}^{o}withx-axis{23.92}^{o}withy-axis$
• D. ${23.92}^{o}withx-axis,{47.16}^{o}withy-axis$

Answer 1

Answer: (A)

${36.87}^{o}withx-axis,{53.13}^{o}withy-axis$

Angle with the $X-axis$

$\Rightarrow tan\theta =\frac{P}{h}=\frac{6}{8}$

$\Rightarrow \theta =ta{n}^{-1}\left(3/4\right)={36.86}^o$

Angle with the $Y-axis$

$\Rightarrow \theta =ta{n}^{-1}\left(3/4\right)={36.86}^o$

$\Rightarrow \alpha ={90}^o-{36.86}^o={53.14}^o$