Resultant Vector Calculation: \( \mathbf{x_R} = (1, -5) \, \text{m} \)

Add the following three vectors to find the resultant vector, xR: x1 = (–2,0)m, x2= (0,–5,)m, x3 = (3,0)m

Group of answer choices

xR = (1, 5)m

xR = (1, –3)m

xR = (1, –0)m

xR = (1, –5)m

To find the resultant vector ( \mathbf{x_R} ), we need to add the three given vectors ( \mathbf{x_1} ), ( \mathbf{x_2} ), and ( \mathbf{x_3} ).

The vectors are:

• ( \mathbf{x_1} = (-2, 0) , \text{m} )
• ( \mathbf{x_2} = (0, -5) , \text{m} )
• ( \mathbf{x_3} = (3, 0) , \text{m} )

Now, we can add the vectors component-wise:

1. Add the x-components: [ x_R = x_1 + x_2 + x_3 = -2 + 0 + 3 = 1 ]

2. Add the y-components: [ y_R = y_1 + y_2 + y_3 = 0 + (-5) + 0 = -5 ]

Putting it all together, the resultant vector ( \mathbf{x_R} ) is: [ \mathbf{x_R} = (1, -5) , \text{m} ]

Thus, the correct answer is: [ \mathbf{x_R} = (1, -5) , \text{m} ]