Question

Vector A⃗ points in the negative y direction and has a magnitude of 5 km. Vector B⃗ has a magnitude of 15 km and points in the positive x direction.

Use components to find the magnitude of A⃗ −B⃗ .

Answer 1

magnitude of A − B = 15.81 km

Step-by-step explanation:

Vector A points in the negative y-direction and has a magnitude of 5 km. Vector B points in the positive x-direction and has a magnitude of 15 km.

According to Cartesian coordinate system, the resultant will start either from tail of A and ends at head of B and vice-versa.

A(0,-5)

B(15,0)

A - B = (-15 i - 5 j )

Magnitude of the vector is given by

|A - B| =
`\sqrt{(-15)^(2)+(-5)^(2)}`

|A - B| =
`√(250)`

|A - B| = 15.81 km