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 ?
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 is . Dividing each component by gives , choice D. Check: . Choice A, , divides by and has magnitude . Choice B is the original vector with magnitude . Choice C, , divides by , which is the magnitude squared, and has magnitude . Only choice D has length exactly .
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