vector J is 3250m long in a 38.4 direction. Vector K is 1822 m long in a 58.8 direction. Find the magnitude and direction of their vector sum

The resultant vector has a magnitude of 4998 m and a direction of 45.7°.

Explanation:

The x component of the resultant vector is the sum of the x components of each individual vector.

x = 3250 cos 38.4 + 1822 cos 58.8

x = 3490.8

Similarly, the y component of the resultant vector is the sum of the y components of each individual vector.

y = 3250 sin 38.4 + 1822 sin 58.8

y = 3577.2

The magnitude can be found with Pythagorean theorem:

√ (x² + y²)

√ (3490.8² + 3577.2²)

4998

The direction can be found with trigonometry:

atan (y / x)

atan (3577.2 / 3490.8)

45.7°

The resultant vector has a magnitude of 4998 m and a direction of 45.7°.