Question

Determine the magnitude of the sum of the two vectors:

2.5Î+1.8Ĵ
-6Î-0.7Ĵ
a. 3.67
b. 7.96
c. 4.63
d. 8.86

Answer 1

To find the magnitude of the sum of two vectors, you need to add the components of the vectors along each direction separately and then calculate the magnitude using the formula. In this case, the magnitude of the sum of the two given vectors is approximately 3.67.

Step-by-step explanation:

To find the magnitude of the sum of two vectors, you need to add the components of the vectors along each direction separately.

Given the vectors:

V1 = 2.5Î + 1.8Î - 6Î - 0.7Î

You can add the Î components and the Î components separately:

Îtotal = 2.5 - 6 = -3.5Î

Îtotal = 1.8 - 0.7 = 1.1Î

The magnitude of the sum of the two vectors is equal to the square root of the sum of the squares of the components:

|V1| = sqrt((Îtotal)**2 + (Îtotal)**2) = sqrt((-3.5)**2 + (1.1)**2) ≈ 3.67

Therefore, the magnitude of the sum of the two vectors is approximately 3.67.