ACT Math · Matrices and vectors

What is the unit vector in the same direction as u = (6, 8)?

What is the unit vector in the same direction as u=(6,8)u = (6, 8)?

Answer and explanation

Answer: D: (0.6, 0.8)

A unit vector in the same direction divides the vector by its magnitude. The magnitude of (6,8)(6,8) is 62+82=100=10\sqrt{6^2+8^2}=\sqrt{100}=10. Dividing each component by 1010 gives (0.6,0.8)(0.6,0.8), choice D. Check: 0.62+0.82=0.36+0.64=10.6^2+0.8^2=0.36+0.64=1. Choice A, (3,4)(3,4), divides by 22 and has magnitude 55. Choice B is the original vector with magnitude 1010. Choice C, (0.06,0.08)(0.06,0.08), divides by 100100, which is the magnitude squared, and has magnitude 0.10.1. Only choice D has length exactly 11.

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