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✏️
Vectors
· Examples✏️ Worked Examples — Step by Step
E1
EasyMagnitude of (5, 12):
💡 √(x² + y²).
👁 Show Solution
√(25 + 144) = √169 = 13. ✅ Answer: 13
✅13
E2
MediumDot product (2, −1, 3) · (4, 5, −2):
💡 Sum of component products.
👁 Show Solution
8 − 5 − 6 = −3. ✅ Answer: −3
✅−3
E3
ChallengingFind angle between (1, 0) and (1, 1):
💡 cos θ = a·b / (|a||b|).
👁 Show Solution
cos θ = (1+0) / (1 · √2) = 1/√2 → θ = 45°. ✅ Answer: 45°
✅45°