1. Work out which pair gives you… 1.Dot prod. = 13 2.Dot prod. = 17 3.Dot prod. = 12 4.An obtuse angle

2. Vectors 6 More on scalar product & shortest distance Know how to find acute angles Understand how to dot product line equations Be able to find the shortest distance between a fixed point and a line

3. Obtuse or Acute? There are situations where you’re given a set of vectors that give you an obtuse angle, but you’re asked for the opposite, an acute angle. Say the angle between A and B is 160˚ but they want an obtuse

4. Obtuse or Acute? To find acute angle: 180 – your obtuse angle It’s also always the case that your dot product gives you: An acute angle if it’s positive; Or an obtuse angle if it’s negative

5. Line equations To do scalar product with line equations All that matters is the free vector. Do scalar product with these.

6. What about skew lines? Can you find the dot product or the angle between two lines that don’t intersect?

7. Have a go at the Questions

8. Shortest distance The shortest distance from a fixed point to a line is given by the distance along the perpendicular from the point to the line.

9. Example Find the shortest distance between A (3,5,2) to the line A P O

10. Example Find the shortest distance between A (3,5,2) to the line A P

11. Example Find the shortest distance between A (3,5,2) to the line A P

12. Shortest distance Step 1: squish your line equation together Step 2: Take away your point from above Step 3: Do the scalar product with free vector Step 4: Solve for unknown/scaler and find magnitude of equation in step 2

13. Have a go at the following questions Core 4 Text book Exercise I p 131

14. Homework You can’t spell homework without meow Vectors test next week! Vectors HWK is on moodle (probably)