Question

(b) Use the right-hand rule to decide whether the components of a × b are positive, negative, or 0.

Answer 1

(a)

Given:  

$\vec{a}$ is in xy plane and $\vec{b}$ is in the direction of k.

|a|=6 units, |b|=3 and θ = 90°

|a × b| = |a| × |b| sinθ  

          = |a| × |b| sin90°  

          = 6 × 3 × 1  

|a × b| = 18  

(b)

Let $\vec{c}=\vec{a} \times \vec{b}$

$\vec{c}$ is perpendicular to both $\vec{a} \text { and } \vec{b}$.

In this case,

x-component of $\vec{a} \times \vec{b}$ is positive.

y-component of $\vec{a} \times \vec{b}$ is negative.

z-component of $\vec{a} \times \vec{b}$ is zero.