Vectors

Question 1

Magnitude Formula

Answer 1

Square root of a squared plus b squared plus c squared.

Question 2

Adding, Subtracting and Multiplying Vectors

Answer 2

You add, subtract and multiply each individual component.

Question 3

Position Vectors

Answer 3

If the journey from a vector is A>B, then the position vector can be solved as (b-a).

Question 4

Proving Colinearity

Answer 4

Find A>B, using position vectors, then B>C, using position vectors. Then take a common factor of a vector, and do 2A>B = B>C (opposite one) therefore parallel. Common point of B means points are colinear.

Question 5

Dividing Lines in a Ratio

Answer 5

Make a sketch and plot out the points and ratio. Equate the position vectors and cross multiply. Convert and multiply out, make equal to unknown point algebraically, insert values and solve accordingly. Give co-ordinates if required.

Question 6

When can the scalar product be performed?

Answer 6

When vectors are both pointing in our out of angle, if not, the answer should be negative.

Question 7

Dot Product in Component Form

Answer 7

Multiply each component together and then add together to get answer, such as (a1a1+a2a2+a3a3).

Question 8

Find Angle in Scalar Product

Answer 8

cos0=dot product divided by magnitude of two values. Remember to go cos-1(Ans) at the end.

Question 9

Perpendicular Vectors

Answer 9

Vectors are perpendicular if dot product is equal to zero.

Question 10

Properties of Scalar Product

Answer 10

a.a is the same as a^2. Brackets can be multiplied out.

Question 11

Finding A Ratio (Given Colinear Points)

Answer 11

If they are colinear, there is a k factor of a position vector. You want to solve this k, by simplifying down and working algebraically using the first component of each. Once found k, rewrite and bring down to cross multiply method. Display as 2:1 etc.