Equations

Question 1

Formula for P distance from Origin

Answer 1

r^2 = x^2 + y^2 + z^2

Question 2

Angle OP makes with each axis

Answer 2

cos(thetre) = (x,y or z)/r(length of OP)

Question 3

3D axis symbols

Answer 3

z axis - gamma
y axis - beta
x axis - alpha

Question 4

angle relationship

Answer 4

cos^2 (alpha) + cos^2 (beta) + cos^2 (gamma) = 1

Question 5

Finding the unit vector

Answer 5

divide x, y and z by each respective modulus.

Question 6

Vector addition

parallelogram rule

Answer 6

A + B = (a1 + b1, a2 + b2, a3 + b3)

Question 7

Associative Law for addition of vectors

Answer 7

(a + b) + c = a + (b + c)

It doesn’t matter which order you add you still get the same vector.

Question 8

Distributive law

Answer 8

(lander)(a + b) = (lander)a + (lander)b

Question 9

How to convert a vector with magnitude and direction into cartesian form

Answer 9

Find unit vector in direction then multiply by magnitude

Question 10

Work done equation

Answer 10

((mag of) a)((mag of) F)(cos(thetre))

Question 11

a.b

Answer 11

a1b1 + a2b2 + a3b3

Question 12

cross product

Answer 12

a x b = |a| |b| sin(thetre) â

where a and b are vectors and
where â is normal to vectors a and b

Question 13

cross product area of a parallelogram

Answer 13

A = a x b

where a and b are vectors

Question 14

cross product area of triangle

Answer 14

A = 0.5(a x b)

where a and b are vectors

Question 15

unit vectors

i . i

Answer 15

1

Question 16

unit vectors

i . j

Answer 16

0

Question 17

unit vectors

i x i

Answer 17

0

Question 18

unit vectors

i x j

Answer 18

k

Question 19

cross product in component form

Answer 19

(a2b3-a3b2)i - (a1b3-a3b1)j + (a1b2-a2b1)k

Question 20

orthogonality with cross product unit vectors

Answer 20

clockwise is positive anti clockwise is negative.

eg
i x j = k, j x k = i, k x i = j

where as

j x i = -k, k x j = -i, i x k = -j

Question 21

cross product distributive law

Answer 21

a x (b+c) = (a x c) + (b x c)

Question 22

Principle of transmissibility

Answer 22

when finding moment of a force

M = r1 x F = r2 x F =… = rn x F

therefore we find the easiest value of r to use, often one of the axis in the plane the force intercepts

Question 23

component of force in another vector

Answer 23

(a.b)/(mag of b)

Question 24

vector triple product

Answer 24

(a x b) x c = b(a.c) - a(b.c)