Question
for v=4i-8j, find the unit vector u in the direction of v
Answers
GPT 3.5
To find the unit vector u in the direction of v, we need to first calculate the magnitude of v and then divide each component of v by the magnitude.
Given v = 4i - 8j
The magnitude of v is given by:
|v| = sqrt((4)^2 + (-8)^2)
|v| = sqrt(16 + 64)
|v| = sqrt(80)
|v| = 8.944
To find the unit vector u in the direction of v, divide each component of v by the magnitude:
u = v / |v|
u = (4i - 8j) / 8.944
u = (4/8.944)i - (8/8.944)j
u ≈ 0.448i - 0.894j
Therefore, the unit vector u in the direction of v is approximately 0.448i - 0.894j.
Given v = 4i - 8j
The magnitude of v is given by:
|v| = sqrt((4)^2 + (-8)^2)
|v| = sqrt(16 + 64)
|v| = sqrt(80)
|v| = 8.944
To find the unit vector u in the direction of v, divide each component of v by the magnitude:
u = v / |v|
u = (4i - 8j) / 8.944
u = (4/8.944)i - (8/8.944)j
u ≈ 0.448i - 0.894j
Therefore, the unit vector u in the direction of v is approximately 0.448i - 0.894j.