Yr 2 Vectors

Question 1

How to find area of triangle using vecotr product

Answer 1

Remember length of vector product = parallelogram = 2x area of triangle

So length. Doctor product / 2

Question 2

Make sure to sue the vectors and not random coordinate points

Answer 2

So funky work them out

Question 3

How to find Cartesian equation of plane using vector product and coordinates

Answer 3

Find vectors
Cross product
Now you have normal vector so have x y z part
Can do a dot n to find d
But easier to just sub in a coordinate to get d

Question 4

How to chekc if vector product is correct

Answer 4

Use scale product to make sure itszero

Question 5

Distance point ti plane

Answer 5

Sub point in, mod the plane

Question 6

Distance point to line

Answer 6

Sub point in line

Mod the line

Divide

Question 7

Distance poijt to 3d line vector product

Answer 7

(P-a) x d modded

/ mod d

Where p is point, a is on line , d is direction vector of line

Question 8

Distance point to 3d line using lambda
Coo Dienste of M too

Answer 8

Find the point M which is intersection of line and line from point using lambda ideas

Find PM therefore

Now PM dot with direction vector perpendicular so must be 0, now have lambda

Can now find Pm and thus mod of it which is the question
- but aldo the coordinat of M

Question 9

Parallel line distance?

Answer 9

Same distance everywhere, so just take a point from one line and do same formual as before

Question 10

How to find distance between skew lines

Answer 10

Itd (d1xd2) dot (A1-a2)/ mod (d1xd2)

Remember ti find skew make them equal must be consistent