If v = (2, -5), find the magnitude and direction angle of 2v.

Answer 1

To find the magnitude of 2v, we need to multiply the components of v by 2 and then take the square root of the sum of the squares.

2v = 2(2, -5) = (4, -10)

Magnitude of 2v = √(4^2 + (-10)^2) = √(16 + 100) = √116 = 2√29

To find the direction angle of 2v, we use the formula:

Direction angle = tan^(-1)(y/x)

Here, x = 4 and y = -10

Direction angle = tan^(-1)(-10/4) = tan^(-1)(-5/2) ≈ -68.2 degrees (rounded to one decimal place).

Therefore, the magnitude of 2v is 2√29 and the direction angle is approximately -68.2 degrees.