help with QUATERNIONS :S (1 Viewer)

[kchap42]

Hey can anyone help me/show me how to do this questions to do with Quaternions...

Lex x and y be two quaternions
x = x<SUB>0</SUB> + x<SUB>1i</SUB> + x<SUB>2j</SUB> +x<SUB>3k</SUB>
y = y<SUB>0</SUB> + y<SUB>1i</SUB> + y<SUB>2j</SUB> + y<SUB>3k</SUB>


Find x.y

The 4 numbers are l, i, j and k and have the following properties:
l<SUP>2</SUP> = l (1)
l<SUP>2</SUP> = j<SUP>2</SUP> = k<SUP>2</SUP> = ijk = -1 (2)
li = il
lj = jl
lk = kl
ij = -ji = k
i(jk) = (ij)k = ijk

all real and comlex numbers do commute with i, j and k but they are not commutative with each other.

hope someone can help... thanks :S

 

[darkliight]

(a + bi + cj + dk)(w + xi + yj + zk) = aw + axi + ayj + azk + bwi + bxi^2 + ...

Then tidy using the rules you have, eg, bxi^2 + -bx.

Your rule (2) has a typo too, it should be i^2, not 1^2.

 

[Slidey]

(a + bi + cj + dk)(w + xi + yj + zk) = aw + axi + ayj + azk + bwi + bxi^2 + ...

Then tidy using the rules you have, eg, bxi^2 + -bx.

Your rule (2) has a typo too, it should be i^2, not 1^2.

That's an el not a one.

 

[darkliight]

Should be an i still ... not sure where that el is coming from in his list of rules.
The el's below rule (2) should be 1's though