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A Level Further Maths > Vectors > Flashcards

Vectors Flashcards

1
Q

How many different ways are there to derive a vector equation?

A

2

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2
Q

What does the first way to derive a vector equation need to be done?

A

Given 1 position vector
Given 1 parallel vector to the line

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3
Q

A vector equation of a straight line passing thought the point A, with position vector a, and parallel to the vector b is:

A
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4
Q

What is the purpose of the scalar parameter?

A

By taking different values of the parameter, you can find the position vectors of different points on that straight line

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5
Q

What do you need to derive a vector equation using the second method?

A

2 position vectors?

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6
Q

A vector equation of a straight line passing through the points C and D with position vectors c and d respectively is:

A
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7
Q

How can you work out the cartesian equation of a vector equation?

A
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8
Q

What does “2 points are collinear” mean?

A

The 2 points are on the same straight line

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9
Q

What is the vector equation of a plane

A
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10
Q

What is the explanation of the vector equation of the plane?

A
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11
Q

What do you need to be given to derive the vector equation of a plane?

A

A position vector in the plane
2 non parallel, non zero vectors in the plane

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12
Q

What is the normal vector?
How is it usually written?

A

A vector that is perpendicular to the plane

The normal vector is usually written as n

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13
Q

What is the cartesian equation of a plane in the 3D?

A
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14
Q

How is a plane generally denoted?

A

A capital pi

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15
Q

What does coplanar mean?

A

Points are coplanar if they all lie on the same plane

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16
Q

What is the angle between 2 vectors?

A

The angle is the angle between the way that they are both pointing

17
Q

What is the scalar product often called?

A

The dot product

18
Q

How is the scalar product defined?

A
19
Q

What do you know about the dot product when 2 vectors are perpendicular?

Explain the logic

A

If 2 vectors are perpendicular then you will have cos90
Since cos90=0 the dot product of perpendicular vectors is always 0
Therefore the non zero vectors of a and b are only perpendicular if a.b=0

20
Q

What do you know about the dot product when 2 vectors are parallel?

Explain the logic

A

If 2 vectors are perpendicular then you will have cos90
Since cos90=0 the dot product of perpendicular vectors is always 0
Therefore the non zero vectors of a and b are only perpendicular if a.b=0

21
Q

What is the simple form of the dot product?

A
22
Q
A
23
Q

With all formulas in 9.4 how do you find the obtuse angle?

A

Use the formula to find the acute angle ,x, then do 180-x=y

24
Q

What is the scalar product form of a plane?

A
25
Q

Explain how we know the scalar product form of a plane?

A
26
Q

How can you convert between scalar and cartesian form for the equation of a plane?

A
27
Q

What is a common mistake that I often make?
(Vectors)

A

I forget that they a lot of vectors are position vectors

28
Q
A
29
Q
A
30
Q

What is the algorithm that can be used to determine points of intersection?

A
31
Q

What does it mean if 2 lines are skew?

A

Two straight lines are said to be skew if they are not parallel and they do not intersect

32
Q

What 3 perpendicular distances do you need to be able to calculate?

A

Between 2 non intersecting lines
Between a line and a point
Between a point and a plane

33
Q

What is the method to find the perpendicular distance between two non intersecting lines?

A

For this type of question you find the general vectors OA and OB by making r equal to one vector by adding the position and direction vectors of each equation then find AB in terms of the different parameters. Now you know that the angle between line 1 and AB is 90 so you can calculate the dot product of AB.(the direction vector of line 1) which will equal 0. You can then find the dot product of AB.(the direction vector of line 2). Now you can solve the simultaneous equations for the parameters and then substitute your values back into the position vector AB. Then find the modulus of AB as the distance between then 2 lines

34
Q

What is the method to find the perpendicular distance between a line and a point?

A

This uses the same method as a line and line but there will only be 1 vector equation and therefore only 1 parameter to solve for. Since there is only 1 line you only need to do the dot product with AB.(the direction vector of that 1 line) this will allow you to solve for the parameter and therefore sub into AB and find the modulus

35
Q

What is the method to find the perpendicular distance between a point and a plane?

A

Use the formular:

A Level Further Maths (20 decks)

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