Question

You are given two vectors $\mathbf{a}=(2,3,4)$ and $\mathbf{b}=(0,2,1)$

Which of the following is/are true?

1. a is perpendicular to b.
2. The angle between a and b is $\arccos \left(2\sqrt{\frac{5}{29}}\right)$
3. The vector $\mathbf{a}+2\mathbf{b}$ is parallel to vector b
4. The direction cosines of the vector a+b are $\arccos \left(\frac{2}{3\sqrt{6}}\right)$, $\arccos \left(\frac{5}{3\sqrt{6}}\right)$ ,and $\arccos \left(\frac{5}{3\sqrt{6}}\right)$
5. $\frac{1}{2}\mathbf{a}-\frac{1}{3}\mathbf{b}=\left(1,\frac{13}{6}, \frac{7}{3}\right)$