Question

Consider the two vectors, A = -3.071+ -1.97j and B = -1.24i + -5.71j.

What is the magnitude of C = A + B?

Answer 1

The magnitude of vector C, which is the sum of vectors A and B, is approximately 8.8205.

Step-by-step explanation:

To find the magnitude of vector C, which is the sum of vectors A and B, we will use the Pythagorean theorem. The components of vector C are obtained by adding the corresponding components of vectors A and B. Therefore, Cx = -3.071 - 1.24 = -4.311 and Cy = -1.97 - 5.71 = -7.68.

Now, using the formula for the magnitude of a vector, which is the square root of the sum of the squares of its components, we have:

|C| = sqrt((-4.311)^2 + (-7.68)^2) = sqrt(18.615 + 59.0656) = sqrt(77.6806) = 8.8205.

The magnitude of vector C, therefore, is approximately 8.8205.