Question

Two vectors A and B are added to give a resultant R. The components of A are Ax = -8.0 units and Ay = 6.0 units and the components of B are Bx= 1.0 units and By=- 1.0 units. What is the magnitude of vector R?

Answer 1

Answer:

10.09 units

Explanation:

For the A

Ax = -8.0 units

Ay = 6.0 units

The resultant vector = Ra = $\sqrt{A^2_{x} + A^2_{y} }$

Ra = $\sqrt{(-8)^2 + 6^2 }$ =  10 units

For B

Bx = 1.0 units

By = -1.0 units

The resultant vector = Rb = $\sqrt{B^2_{x} + B^2_{y} }$

Rb = $\sqrt{1^2 + (-1)^2 }$ = $\sqrt{2}$ units

Adding these two vectors A and B together, magnitude of vector R is

R = $\sqrt{R^2_{a} + R^2_{b} }$

R =  $\sqrt{10^2 + (\sqrt{2} ) ^2}$ = 10.09 units