Find the sine of the angle between the vectors and

We have

Let these vectors be represented as,

Comparing the vectors, we get

a₁ = 3, a₂ = 1 and a₃ = 2

b₁ = 2, b₂ = -2 and b₃ = 4

To find sine of the angle between the vectors and , we can first find out cosine of the angle between them.

Cosine of the angle between and is given by,

[∵ we know that, and .

So,

Also, we know that, ]

By algebraic identity, we have

Thus, sine of the angle between the vectors is .