find the resultant and direction of2 vectors of 3units and4unit acting at a point o at an angle of 45 with each other with cosine rule

Answer 1

Using the cosine rule, we can find the magnitude of the resultant vector:

$r^2 = 3^2 + 4^2 - 2(3)(4)\cos(45^\circ)$

$r^2 = 25 - 12\sqrt{2}$

$r \approx 1.86$

To find the direction of the resultant vector, we can use the sine and cosine functions:

$\theta = \sin^{-1}\left(\frac{3\sin(45^\circ)}{r}\right)$

$\theta \approx 26.57^\circ$

Therefore, the resultant vector has a magnitude of approximately 1.86 units and points in a direction of approximately 26.57 degrees (measured counterclockwise from the positive x-axis).