Did you read my tips on how to study and learn Math 1300?  If not, here is a link to those important suggestions:

Did you see my tips for Assignment 1? Click here.

Here is a link to the actual assignment, in case you don't have it handy:

Don't have my book or audio lectures?  You can download a free sample of my book and audio lectures containing Lessons 1, 2 and 9:

Similar to my Lesson 10, question 4.

Again, similar to my Lesson 10, question 4.

Make sure you have read my discussion on pages 333 to 336 to understand how you can tell if lines and/or planes are parallel or perpendicular.  Otherwise, this is basically a combination of my questions 5 and 10.  There are also several of my Practise Problems that deal with similar concepts.

Skew lines are lines that are not on the same plane (therefore they will never intersect), but are not parallel.  For example, visualize a line drawn from east to west on the floor.  Now visualize drawing a diagonal line on the ceiling.  Those lines are not parallel to each other, but they would never intersect either.  Keep that visual image in your head as you do this problem

This is just some basic principles of reading off info from the equation of a line.  You learned how to get the sine of the angle between two vectors in Lesson 9.  Note that the vector PQ forms the hypotenuse of a right triangle, and the side of the right triangle that is parallel to the normal vector you found earlier, is the distance between the two lines.

You can use trigonometry to find that distance (that is why they had you find the sine of that angle earlier), or you can also use the projection vector formula I taught you in Lesson 9.  Find the projection of PQ onto n.  The length of that projection vector is the distance you seek.

Your course notes also give you a formula for finding the distance between a point and a line that can also be used here, too, if you wish, but, they have pretty much guided you through all of that formula in the previous parts of the question.

Part (a) is very similar to my Practise Problem 22(b).

Part (b) is like my question 5 in the Lecture Problems.

Note that there will be the unknown value a in the two vectors you come up with in part (a).  Then you will solve for a in parts (b) and (c) using what you should know about what is necessary for vectors to be parallel or perpendicular.

Part (d) uses the formula for the cosine of an angle between two vectors as memorized in Lesson 9.  The dihedral angle is simply the angle made by the two planes.  It is also the angle between the two planes' normal vectors.