Question

Consider the vectors u = <-4, 7> and v = <11, -6>. Find u + v and |u + v|.

A. u + v = <7, 1>, |u + v| = √50 units
B. u + v = <7, 1>, |u + v| = 7 units
C. u + v = <7, 1>, |u + v| = √10 units
D. u + v = <7, 1>, |u + v| = √58 units

Answer 1

To find the sum of vectors u and v, add their corresponding components. The magnitude of the sum can be found using the Pythagorean theorem.

Step-by-step explanation:

To find the sum of two vectors, u and v, we add their corresponding components. For u = <-4, 7> and v = <11, -6>, we add the x-components and the y-components separately:

u + v = x + vx, uy + vy> = <-4 + 11, 7 - 6> = <7, 1>

To find the magnitude of the sum of two vectors, we use the Pythagorean theorem:

|u + v| = √(ux + vx)2 + (uy + vy)2 = √(7)2 + (1)2 = √50 units