Question

Find the magnitude and direction angle of the resultant vector.

7) First vector: (8,240°)
Second vector: (10, 80°)

Answer 1

9514 1404 393

Answer:

3.694∠127.8°

Explanation:

A suitable calculator makes short work of this.

(8; 240°) +(10; 80°) ≈ (3.694; 127.8°)

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If you like, you can add the components of the vectors and figure the magnitude and direction of the result.

a = 8(cos(240°), sin(240°)) ≈ (-4.0000, -6.9282)

b = 10(cos(80°), sin(80°)) ≈ (-1.7365, 9.8481)

r = a + b ≈ (-2.2635, 2.9199)

|r| = √(2.2635² +2.9199²) ≈ 3.69448

∠r = arctan(2.9199/-2.2635) ≈ 127.783°

The resultant is approximately 3.694∠127.78°.