Find the unit vector in the direction of vector a = (6, -8).
Answer and explanation
Correct answer: C. (3/5, -4/5)
- Step 1: Find the magnitude of a: ||a|| = sqrt(6^2 + (-8)^2) = sqrt(36 + 64) = sqrt(100) = 10.
- Step 2: The unit vector is a / ||a|| = (6/10, -8/10) = (3/5, -4/5).
Answer
(3/5, -4/5).
Why not the others: '(6/10, 8/10)' flips the sign of the y-component; '(4/5, -3/5)' swaps the x and y coordinates; '(-3/5, 4/5)' points in the opposite direction.
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