Question

For direction vectors \[\vec b_1=(1,2,2)\] and \[\vec b_2=(3,2,6)\], the angle between the lines is:

Options

• \[\theta=\cos^{-1}\left(\frac{19}{21}\right)\]

• \[\theta=\sin^{-1}\left(\frac{19}{21}\right)\]

• \[\theta=\cos^{-1}\left(\frac{21}{19}\right)\]

• \[\theta=\cos^{-1}\left(\frac{19}{7}\right)\]

Answer 1

Using the dot-product formula gives \[\cos\theta=\left|\frac{19}{3\cdot7}\right|=\frac{19}{21}\]. Therefore, \[\theta=\cos^{-1}\left(\frac{19}{21}\right)\].