Wayground Vector Quiz
Flashcard
•
Mathematics
•
10th Grade
•
Practice Problem
•
Hard
Mathdepartment2025 Mathdepartment2025
Used 1+ times
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10 questions
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1.
FLASHCARD QUESTION
Front
Find the unit vector in the direction of **a = 2i – 4j**.
Back
Magnitude = √(2² + (–4)²) = √20 = 2√5.
Unit vector = (1/2√5)(2i – 4j) = (1/√5)(i – 2j)
2.
FLASHCARD QUESTION
Front
If **a = 2i – 4j**, **b = i – 2j**, and **c = [1, 3]**, find the unit vector in the direction of **a + b + 2c**.
Back
a + b + 2c = (2 + 1 + 2)i + (–4 – 2 + 6)j = 5i + 0j
Magnitude = 5 → Unit vector = î
3.
FLASHCARD QUESTION
Front
If **a = i – 3j** and **b = 2i + 4j**, find a vector of magnitude **4** in the direction of **2a – b**.
Back
2a – b = (2 – 2)i + (–6 – 4)j = –10j
Unit vector = –ĵ
Vector = 4(–ĵ) = –4ĵ
4.
FLASHCARD QUESTION
Front
Solve for **k** if **3i + kj ∥ 12i + 8j.**
Back
Ratio of i-components = 12 ÷ 3 = 4.
So k = 8 ÷ 4 = **2**.
5.
FLASHCARD QUESTION
Front
If **a = i – 3j** and **b = 2i + 4j**, find a vector of magnitude **6** in the opposite direction of **a + 2b.**
Back
a + 2b = (1 + 4)i + (–3 + 8)j = 5i + 5j
Unit vector = (1/√50)(5i + 5j) = (1/√2)(i + j)
Opposite direction = –(1/√2)(i + j)
Vector = 6 × (–1/√2)(i + j) = –3√2(i + j)
6.
FLASHCARD QUESTION
Front
What is the formula for a **unit vector**?
Back
7.
FLASHCARD QUESTION
Front
What is the magnitude of the vector **3i – 4j**?
Back
Magnitude = √(3² + (–4)²) = **5**
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