To find a unit vector in the direction of (3, -1, 2, 4), we must first calculate the magnitude of the given vector. The magnitude of a vector (3, -1, 2, 4) is given by the formula:
|v| = sqrt(3^2 + (-1)^2 + 2^2 + 4^2)
|v| = sqrt(9 + 1 + 4 + 16)
|v| = sqrt(30)
To find the unit vector, we divide each component of the given vector by its magnitude:
u = (3/|v|, -1/|v|, 2/|v|, 4/|v|)
u = (3/sqrt(30), -1/sqrt(30), 2/sqrt(30), 4/sqrt(30))
Therefore, a unit vector in the direction of (3, -1, 2, 4) is approximately (0.547, -0.182, 0.365, 0.730).
Find a unit vector in the direction of (3, -1, 2, 4)
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