Cheers Eric, I'm familiar with how to calculate the scalar product of vectors in two dimensions but I'm not completely sure on how to tackle questions with 3 dimensions. I assume its a similar process but I don't have answers to the questions
Yep, Eric's right. Just a bit of background knowledge:
We only multiply the parallel components (that is, i with i, j with j, k with k) because theta = 0 so cos(theta)=1. The perpendicular components (eg i and j) are perpendicular so cos(theta)=0. You should remember that a.b=|a||b|cos(theta) which is why we do this.
So (2i+3j).(2i+3j)=2i.2i+2*2i.3j+3j.3j = 4+0+9 = 13. (You don't have to do this in the exam or anything)
So just multiply the coefficients for each unit vector, as Eric said
You can do this for vectors in as many dimensions as you like, even higher than 3