Vectors And Scalar Product

Question 1

What is the cosine rule

Answer 1

A2 = b2 +c2 -2bc cos A

-!

Question 2

Same for 3d, dot product / mods

Answer 2

And remember it’s mods

Question 3

Remember fir triangle area use mods of two sides which are

Answer 3

Perpendicular to each other

Question 4

Prove perpendicular what?

Answer 4

Dot product is 0

Question 5

Cartesian equation from a plane

Answer 5

1) first need position vector to identify the plane from origin , A

2) then we know normal vector is normal to every point in plane
3) need a vector to get to any general point on the plane now , call it r

So the vector from a to r is R-a

And any point here will be perpendicular to n

So n -[r-a] =0

Now this is distributive, meaning n-R -(n-A) is the same and this = 0

Question 6

Remember that equation is n dot (r-a) so

Answer 6

If in vector form like that don’t be scared, identify n, identify NEW a if it is parallel and do , don’t worry

Question 7

Angle between planes?

Answer 7

Is the same as angle between both NORMAL VECTORS

Question 8

Okay so remember angle between planes

Answer 8

Is given by angle between normals

However, this may be the OBTUSE ANGKE

If they say Accure, gotta do 180-x for that!

So remember this tricj

Question 9

Ahhh remember about finding triple simultaneous answers when only 2 expressions

Answer 9

Here you gotta make sure ti remember to MAKE THEM ALL ONE VARIABLE AND REMEMBER

Then sub back into equation

2) now using VALUE THEY GAVE, CAN WORK OUT D ASWELL

And can canecel them all tk ger equation

Remember to sub in and can jus cancel straight away,

MAKE SURE TOU ELIMINATE INE VARIABEL FIRSR THROUGH MANIPULATION ADN ADDITION

OR IF THREE, DO MATRICY SOLUTION AND TAKE VARIABLE TO BE 1

Question 10

How to do vector for,

Answer 10

Just n dot r -(n dot a)

And do r dot n = d

Question 11

PAST PAPER MISTAKES

Answer 11

make sure to show the PARALLELOGROM WHEN DOING COMPLEX NUMBER SDDTION SUBTRACTION KN ARGAND

Question 12

Remember swaure complex number

Answer 12

You get swaure + saaure