Question

Given the vector u equal to 4 (cos 175°, sin 175°) and vector v equal to 5 (cos 65º, sin 65°), find the sum u + v and write your answer in magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree.

Answer 1

To find the sum u + v, add the corresponding components separately. Use the Pythagorean theorem to find the magnitude and the inverse tangent function to find the direction.

Step-by-step explanation:

To find the sum u + v, we can add the corresponding components of the vectors u and v separately. The x-component of u is 4*cos(175°) and the x-component of v is 5*cos(65°). Adding these gives us the x-component of the sum. Similarly, the y-component of u is 4*sin(175°) and the y-component of v is 5*sin(65°). Adding these gives us the y-component of the sum.

Once we have the x and y components of the sum, we can use the Pythagorean theorem to find the magnitude and the inverse tangent function to find the direction. Rounding to the nearest tenth, the magnitude of the sum is approximately 8.7 units and the direction is approximately 9°.