Maths

Question 1

What is the dot product equation?

Answer 1

cos (x) = (a . b)
/Mod(a)Mod(B)

Question 2

For plane ax + by + cz = d what is the normal vector to the plane

Answer 2

n = a , b ,c

Question 3

Line to point (P) distance equation

Answer 3

Mod(PQ x d) / Mod(d)
d= direction vector of line
PQ = vector from point on line to P

Question 4

Line to Line distance equation?

Answer 4

(d1 x d2) = N
Then calculate unit vector of N (n)
n . PQ = distance

Question 5

Plane to point equation

Answer 5

n = unit vector normal to plane
mod(n . PQ) = distance

Question 6

How to tell if vector lies on plane?

Answer 6

Take dot product with normal of plane, if 0 then on plane.

Question 7

What makes vectors linearly independent?

Answer 7

If the only constants to sum the vectors to 0, are trivial solution 0

Question 8

What is typical form of complex number?

Answer 8

z = a + jb

Question 9

Polar form of complex number?

Answer 9

Z = R θ
R = mod(Z)
θ = arctan (b/a)

Question 10

Express complex number in trig functions

Answer 10

Z = R (cos θ + j sin θ)

Question 11

What is the complex conjugate?

Answer 11

Z = a + jb
Conjugate = a - jb

Question 12

Demoive’s theorem

Answer 12

(cosθ + jsinθ)^n = cos(nθ) +
jsin(nθ)

Question 13

Impedance of capacitor?

Answer 13

1/j omega C

Question 14

Impedance of inductor?

Answer 14

j omega L

Question 15

What is omega?

Answer 15

Hz x 2 pi = omega