Math 1300 Distance: Tips for Assignment 2

Published: Sat, 02/08/14

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 read my tips for Assignment 1?  If not, here is a link to those important suggestions:
Tips for Assignment 2
Here is a link to the actual assignment, in case you don't have it handy:
Note that you need to study Lesson 10 (Lines and Planes) from my Linear Algebra & Vector Geometry book to prepare for this assignment.  I think you should find this assignment fairly straightforward if you do thoroughly study and do all the Practise Problems I give you in Lesson 10.
Don't have my book?  You can download a free sample of my book and audio lectures containing Lessons 1, 2 and 9:
Question 1
Very similar to my question 4 in Lesson 10.
Question 2
Part (b) simply requires the cosine of the angle between the two vectors you found in part (a).

Part (c) requires a cross product.  Visualize the two planes (like say the floor in your room and a wall in your room; although your planes aren't intersecting at a right angle).  Visualize their two normal vectors and you should see how their cross product does create a third vector that runs parallel to the line of intersection between the two planes.

Part (d) is just a matter of subbing y=0 into both planes equations and then solving the resulting 2 equations with 2 unknowns.
Question 3
Kind of a combination of my questions 5 and 10 in Lesson 10.  Note that, rather than use the distance from a point to a plane formula I give you in Lesson 10, you can find the distance by projecting vector QP onto the normal vector n.  The length of that projection vector is the distance.
Question 4
Again, just follow their instructions in this problem.  Note that the formula for the sine of the angle between two vectors that you learned in Lesson 9 is relevant here.  Again, the appropriate projection vector will find the distance they desire.
Question 5
Basically a combination of my questions 5 and 6.
Question 6
A pretty standard application of vectors and planes.  Note that the formula you learned for the cosine of the angle between two vectors in Lesson 9 is relevant here.