Question

Find the magnitude and direction of vector R= i+j.​

Answer 1

To find:

Magnitude and direction of vector R = i + j ?

Calculation:

The given vector is :

$\sf \vec{R} = \hat{i} + \hat{j}$

Now, the net magnitude of the resultant:

$\sf | \vec{R} | = \sqrt{ {1}^{2} + {1}^{2} + 2 \times 1 \times 1 \times \cos( {90}^{ \circ} ) }$

$\sf \implies | \vec{R} | = \sqrt{ {1}^{2} + {1}^{2} + 2 \times 1 \times 1 \times 0 }$

$\sf \implies | \vec{R} | = \sqrt{ {1}^{2} + {1}^{2} }$

$\sf \implies | \vec{R} | = \sqrt{1 + 1 }$

$\sf \implies | \vec{R} | = \sqrt{2 }$

Let angle of resultant with $\hat{i}$ be $\theta$:

$\sf \therefore \: \cos( \theta) = \dfrac{1}{ \sqrt{2} }$

$\sf \therefore \: \theta = {45}^{ \circ}$

So, the R vector will be 45° North of East.