1. Multi-dimensional vectors play a far more critical role in electromagnetic theory than in simplemechanics, so some practice is helpful. Recall that there are two types of vector multiplication:the dot

product and the cross product.The dot product of two vectors is a measure of how parallel they are; its magnitude is largestwhen the two vectors are parallel and smallest when they are perpendicular. Since the resultis just a number (not a vector), it is sometimes called the scalar product. For two vectors Aand B, the dot product is mathematically indicated as A · B. The value of the dot productis given by the formula AB cos 0, in which A is the magnitude of A, B is the magnitude of Band 0 is the angle between A and B. (a) Using labeled arrows to represent two vectors A and B, make three sketches, one showingthe two vectors oriented to have a positive dot product, one showing an orientation givinga negative dot product, and one showing an orientation giving a zero value dot product. ) If you have the xyz components of two vectors, you can use this formula to find the dotproduct: A ·B = A„B + AyBy+ A¿Bz. For the vectors A = li+0j+2k and B = 0i+ lj+ 2k, determine the dot product A · B.(Note i, j, k are the unit vectors in the x, y and z directions.) Afteryou have found the dot product, find the angle between the two vectors A and B(hint: you'll need to use an inverse trig function).