   Chapter 12.4, Problem 16E

Chapter
Section
Textbook Problem

# The figure shows a vector a in the xy-plane and a vector b in the direction of k. Their lengths are |a|=3 and |b| = 2.(a) Find |a × b|.(b) Use the right-hand rule to decide whether the components of a × b are positive, negative, or 0. (a)

To determine

To find: The magnitude of cross product |a×b|.

Explanation

Given: |a|=3, |b|=2.

Formula used:

If θ is the angle between the vectors u and v, then the cross product is,

|u×v|=|u||v|sinθ (1)

Here,

|u| is the magnitude of vector u, and

|v| is the magnitude of vector v.

Right-hand rule:

The fingers of the right hand curl in the direction of a rotation from a to b, then the thumb points in the direction of a×b. The rotation angle should be less than 180°.

Redraw the given Figure with indication of angle as shown in Figure 1.

(b)

To determine

To check: Whether the components of a×b are positive, negative or 0.

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