Find the distance between: a) \((3,4)\) and origin; b) \((1,2,2)\) and origin; c) \((1,1)\) and \((4,5)\).
Q2 Prereq — Trig
[3]
Without a calculator: a) Convert 60° to a vector \((x,y)\) of length 10 (use exact values); b) State \(\sin 30°,\cos 30°\); c) State \(\cos 45°\).
Q3 Prereq — Algebra
[2]
Solve \(\sqrt{a^2+9}=5\) for \(a>0\). Solve \(2k=8-3k\).
Q4 Thinking
[3]
Two forces of 5 N each pull on a ring at 90° to each other. Without computing first, predict whether the resultant magnitude is more than, less than, or equal to 10 N. Justify with a sketch description.
Q5 Communication
[3]
Explain in your own words why a vector has both magnitude and direction. How does this differ from a scalar quantity? Give two real-world examples of each.
Q6 Thinking
[3]
Without computing magnitudes, decide which is longer and explain: \(\vec u=(3,4,0)\) or \(\vec v=(2,2,2)\)?
Q7 Reflection
[2]
Vectors are new content. What is your biggest concern as you start? (Algebra? Geometry? 3-D visualization?)
📝 Teacher Feedback
Your teacher will provide feedback after reviewing.