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Higher Maths > Vectors > Flashcards

Flashcards in Vectors Deck (21)
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1
Q

what is a scalar

A

a quantity with a magnitude only

2
Q

what is a vector

A

a quantity with magnitude and direction

3
Q

what is a zero vector

A

any vector with all components zero

4
Q

how do we represent magnitude for vector u?

A

|u|

5
Q

how to calculate the magnitude of a vector

A

the square root of all the components squared

6
Q

what is a unit vector?

A

any vector with a magnitude of one

7
Q

what is the 3-dimensional version of the distance formula?

A

d = square root of (x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2

8
Q

what are equal vectors?

A

vectors with the same magnitude and direction

all components are equal

9
Q

what position do vectors need to be in to add or subtract them?

A

nose to tail

10
Q

what is the negative of a vector?

A

the vector multiplied by 1

11
Q

what is OA (with arrow above)

A

a position vector of point A relative to the origin O, and is written as a

12
Q

what can ai + bj + ck be written as?

A

(a b c)

13
Q

the points A, B and C in 3D space are collinear if…

A

AB is parallel to BC, with B a common point

14
Q

non-zero vectors are parallel if…

A

they are scalar multiples of the same vector

15
Q

steps to find the coordinate of a point which divides a line segment in a given ratio

A
  1. make a sketch
  2. equate the ratio of the two lines with the given ratio
  3. cross multiply and change line segments into position vectors
  4. rearrange
  5. write as a coordinate
16
Q

scalar product formula

A

a.b = |a| |b| cos theta

17
Q

what do you need to remember when calculating scalar product

A

the vectors a and b need to both either be pointing towards or away from the angle

if one is pointing away while the other points towards then a.b = -|a| |b| cos theta

18
Q

the component form of the scalar product

A

a.b = a1b1 + a2b2 + a3b3

19
Q

how to calculate the angle between vectors

A

cos theta = a.b / |a||b|
or
cos theta = a1b1 + a2b2 + a3b3 / |a||b|

20
Q

what is the scalar product when the vectors are perpendicular

A

0

21
Q

properties of the scalar product

A

a. b = b.a
a. (b+c) = a.b + a.c
a. a = |a|^2