✏️ Practice Exercises

Vectors

3 problems · Easy to Hard · Type your working · AI checks your steps

💡

How to use these exercises

Read the question → work it out step-by-step in the box → click Check My Working to get AI feedback. Use hints if stuck. Reveal the full solution only after you have tried.

01

easy

Magnitude of (5, 12):

💡 Show hint

√(x² + y²).

Your Working

02

medium

Dot product (2, −1, 3) · (4, 5, −2):

💡 Show hint

Sum of component products.

Your Working

03

hard

Find angle between (1, 0) and (1, 1):

💡 Show hint

cos θ = a·b / (|a||b|).

Your Working

🏆

Finished all 3 problems?

Head back to the lesson or ask Gani for more help.

🏆 Take the Quiz →🤖 Ask Gani