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

10.09 units

Step-by-step explanation:

For the A

Ax = -8.0 units

Ay = 6.0 units

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

Ra =
`√((-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 =
`√(1^2 + (-1)^2 )` =
`√(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 + (√(2) ) ^2}` = 10.09 units