Find the sine of the angle between the vectors a = 3i + j + 2k and b = 2i - 2j + 4k.

Question

Find the sine of the angle between the vectors \(\vec a = 3 \hat i + \hat j + 2 \hat k\) and \(\vec b = 2 \hat i - 2 \hat j + 4 \hat k\)

Answer 1

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 \(\vec a\) and \(\vec b\), we can first find out cosine of the angle between them.

Cosine of the angle between \(\vec a\) and \(\vec b\) is given by,

By algebraic identity, we have

Thus, sine of the angle between the vectors is 2/√7.