Final answer:
To find | v - 2w |, we need to subtract 2w from v and then find the magnitude of the resulting vector. Given that |v| = 2, |w| = 3, and the angle between v and w is π/3, the magnitude of v - 2w is approximately 4.73.
Step-by-step explanation:
To find | v - 2w |, we need to subtract 2w from v and then find the magnitude of the resulting vector.
Given that |v| = 2, |w| = 3, and the angle between v and w is π/3, we can find the components of v and w as follows:
v = 2cos(π/3)i + 2sin(π/3)j
w = 3cos(0)i + 3sin(0)j
Substituting the values, we get:
v - 2w = (2cos(π/3) - 2 * 3cos(0))i + (2sin(π/3) - 2 * 3sin(0))j
Simplifying the expression:
v - 2w = (2 * 1/2 - 2 * 3 * 1)i + (2 * √3/2 - 2 * 3 * 0)j
Finally, the magnitude of v - 2w is:
| v - 2w | = √((2 * 1/2 - 2 * 3 * 1)^2 + (2 * √3/2 - 2 * 3 * 0)^2)
Calculating the expression, we get:
| v - 2w | ≈ 4.73