Question

Vector u has its initial point at (17,5) and its terminal point at (9, -12). Vector v has its initial point at (12, 4) and its terminal point at (3,-2). Find 113u - 2v11. Round your answer to the nearest hundredth.

A. 29.79 units
B. 32.12 units
C. 39.46 units
D. 42.23 units

Answer 1

To find the vector 113u - 2v11, we find the components of u and v, multiply them by the appropriate scalars, subtract the resulting vectors, and find the magnitude of the final vector.

Step-by-step explanation:

To find the vector 113u - 2v11, we first find the components of u and v. The components of u are (9-17, -12-5) which is (-8, -17). The components of v are (3-12, -2-4) which is (-9, -6). Next, we multiply the components of u by 113 and the components of v by 2 and subtract them to get the components of the final vector:

(113(-8)-2(-9), 113(-17)-2(-6)) = (-190, -197)

Finally, we find the magnitude of the final vector using the distance formula:

|(-190, -197)| = sqrt((-190)^2 + (-197)^2) = sqrt(36169) ≈ 190.42

So, the rounded answer to the nearest hundredth is 190.42 units.