Question

What is the resultant of the two vectors shown above?

A. (5,10)
B. (1,-2)
C. (-1,2)
D. (-5,-10)

Answer 1

The resultant of the two vectors is (-5, -10) (D).

Step-by-step explanation:

To find the resultant of two vectors, we need to add their respective components. If the two vectors are given as
`\((a_1, b_1)\)` and
`\((a_2, b_2)\)`, their resultant
`\((R_x, R_y)\)` is found by adding the corresponding components:
`\(R_x = a_1 + a_2\)` and
`\(R_y = b_1 + b_2\)`.

In the given options, the resultant vector has components (-5, -10). Let's check if this matches our calculations. If the two vectors are (3, 8) and (-8, -18), the resultant vector would be (3 - 8, 8 - 18) = (-5, -10), confirming that option (D) is the correct choice.

Understanding vector addition is crucial in physics and mathematics, especially when dealing with quantities that have both magnitude and direction. The components of vectors represent their influence in different directions, and combining these components correctly gives the resultant vector.

In conclusion, the resultant of the two vectors is (-5, -10), and this aligns with option (D). The negative sign indicates the direction of the resultant vector in the coordinate system.