Diagnostic — checks Unit 6 vector basics + cosine law prereqs
📋 Not Graded
Purpose: Probes Unit 6 magnitude/operations and trig (cosine law) prerequisites for dot/cross product applications.
Q1 Prereq — Unit 6
[3]
For \(\vec u=(2,-1,3)\): a) state \(|\vec u|\); b) state the unit vector \(\hat u\); c) state \(2\vec u\).
Q2 Prereq — Trig
[3]
In a triangle with sides 5, 7, and angle 60° between them, find the third side using the cosine law.
Q3 Prereq — Geometry
[2]
State the area formula for a parallelogram in terms of two adjacent sides \(a, b\) and the included angle \(\theta\).
Q4 Thinking
[3]
Two vectors \(\vec u\) and \(\vec v\) have \(|\vec u|=|\vec v|=4\). Predict whether \(\vec u\cdot\vec v\) could be: a) 16; b) 0; c) -16. Under what conditions?
Q5 Communication
[3]
Define "work" in physics. How does the formula \(W=\vec F\cdot\vec d\) capture the idea that only the component of force along the displacement contributes?
Q6 Thinking
[3]
If \(\vec u\) is in the \(xy\)-plane and \(\vec v=\hat k\), what direction does \(\vec u\times\vec v\) point? Justify using right-hand rule.
Q7 Reflection
[2]
Which feels more confusing right now: dot product or cross product? What aspect specifically?
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