Magnitude of u = sqrt(162). This is correct.

V = (3, -3, -12)/sqrt(162) << I guess you simply forgot the x and y components

or V = (3/sqrt(162), -3/sqrt(162), -12/sqrt(162)) if you wish to express it in component form.

You went wrong in not appreciating that u is a 3-dimensional vector. With reference to 3 mutually perpendicular axes, x, y and z, each contains unit vectors i, j and k respectively.

Therefore, u = 3i - 3 j - 12k.

|u| = √(3² + 3² + 12²) = √(9 + 9 + 144) = √162.

Hence, u / |u| = (3i - 3 j - 12k) / √162.

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