Exercise 1: Vector Addition, Scalar Multiplication, Magnitude & Normalization — Possible Solution
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GIVEN
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c = [6, 8]
d = [-2, 1]

(A) c + d
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Add component by component:
  c + d = [6 + (-2), 8 + 1] = [4, 9]

(B) 3 . d
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Multiply every component by the scalar 3:
  3.d = [3 x -2, 3 x 1] = [-6, 3]

(C) THE MAGNITUDE OF c
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|c| = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10

(D) THE NORMALIZED (UNIT) VECTOR FOR c
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Divide every component of c by its own magnitude (10):
  c / |c| = [6/10, 8/10] = [0.6, 0.8]

Check: sqrt(0.6^2 + 0.8^2) = sqrt(0.36 + 0.64) = sqrt(1) = 1, confirming
this is genuinely a unit-length vector.

WHY THIS WORKS AS AN ANSWER
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Each result applies exactly one of this chapter's own definitions -
component-wise addition, component-wise scalar multiplication, the
Pythagorean-style magnitude formula, and dividing by that magnitude to
normalize - with the normalization result double-checked by
recomputing its own magnitude and confirming it comes out to exactly 1.