Question

5. The analytical method of adding vectors expressed in terms of their components may be applied to vectors in three dimensions, for which graphical work is inconvenient. Find the magnitude of the resultant of the vectors A = i12 —j37 + k58 and B = i5 + j30 — k42, where i, j, and k are unit vectors along the x, y, and z axes, respectively

Answer 1

C = 17 i^ - 7 j^ + 16 k^ , | C| = 24.37

Step-by-step explanation:

To work the vactor component method, we add the sum in each axis

C = A + B = (Aₓ + Bₓ) i ^ + (
`A_(y)` +
`B_(y)`) i ^ + (
`A_(z)` +
`B_(z)`) k ^

Cₓ = 12+ 5 = 17

`C_(y)` = -37 +30 = -7

`C_(z)` = 58 -42 = 16

Resulting vector

C = 17 i ^ - 7j ^ + 16k ^

The mangitude of the vector is

| C | = √ c²

| C | = √( 17² + 7² + 16²)

| C| = 24.37