Wayground Vector Quiz

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)

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

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

Front

Solve for **k** if **3i + kj ∥ 12i + 8j.**

Back

Ratio of i-components = 12 ÷ 3 = 4.
So k = 8 ÷ 4 = **2**.

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)

Front

What is the formula for a **unit vector**?

Back

Front

What is the magnitude of the vector **3i – 4j**?

Back

Magnitude = √(3² + (–4)²) = **5**

Front

An airplane flies at 380 mph on a bearing of 45°. Wind blows at 50 mph on a bearing of 135°. What method can be used to find its actual velocity?

Back

Use the vector diagram and apply the cosine rule or component method to find the resultant velocity and bearing.

Front

How do you find a vector of a given magnitude in a specific direction?

Back

1️⃣ Find the unit vector in that direction.
2️⃣ Multiply by the desired magnitude.

Front

If two vectors are parallel, what is true about their components?

Back

Their corresponding components are in the same ratio.