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Answer :
Final answer:
To find a unit-vector expression for a vector B one-fourth the length of A and pointing in the same direction as A, we divide A by its magnitude and multiply by one-fourth.
Explanation:
To find a unit-vector expression for a vector B one-fourth the length of A and pointing in the same direction as A, we first need to find the length of A. Using the formula for the magnitude of a vector, we have: |A| = sqrt((Ax)^2 + (Ay)^2 + (Az)^2) = sqrt((8.00)^2 + (12.0)^2 + (-4.00)^2) = 14.70 units.
Now, to find B, we can multiply A by one-fourth and divide by the magnitude of A. The unit-vector expression for B is therefore:
B = (1/4)*(A/|A|) = (1/4)*(8.00/14.70)î + (1/4)*(12.0/14.70)Ĵ + (1/4)*(-4.00/14.70)k
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