Question

A vector has component along the $x$-axis equal to $25\text{unit}$ and along the $y$-axis equal to $60\text{unit}$. The magnitude of the vector is

• A. $65\text{unit}$
• B. $55\text{unit}$
• C. $45\text{unit}$
• D. $85\text{unit}$

Answer 1

The correct option is A $65\text{unit}$

The given vector is the resultant of two perpendicular vectos, one along the $x$-axis equal to $25\text{unit}$ and the other along the $y$-axis equal to $60\text{unit}$.
The resultant has a magnitude given by
$\sqrt{{25}^2+{60}^2+2\times 25\times 60\times \cos {90}^{\circ }}$
$\Rightarrow \sqrt{{25}^2+{60}^2}=65\text{unit}$