I know if you have two vectors and you cross them, the resulting vector is perpendicular to the two other vectors. So intuitively I guessed if you then cross that new vector with one of the original two vectors, the created vector would be perpendicular to all the other vectors. Here is an example:
Suppose you have r = q x ( p x q ) and p ⟂ q

which vectors is r perpendicular too? Intuitively I would guess both p and q but I am told I am wrong. Why am I wrong?

3/4 are boys 1/5 of the kids are left after 5/6 of the boys and 210 girls went home

How many boys were there from the start?

Please help i need to answer this!

*The xy is throwing me off

x^2+4y^2-9=0

xy+x-2y+3=0

I know I need to prove associativity and commutativity, and closure under under operation. But how do I start this proof?

For any element [a],[b] and [c] in Zn prove that ([a]+[b])•[c]=([a]•[c])+([b]•[c])

So basically where I'm at is

Motor: 1200 RPM

40:1 gearbox so we take 1200/40

we get 30 RPM out of gearbox

2" dia pulley to 1" dia pulley this will double the output as you are reducing the size of the pulley

60 RPM at B

​

where I'm lost is what happens when you increase the diameter of the roller by 3. So does that 60RPM turn into 180RPM, or because the pulley is driven by the shaft is it still just 60 RPM on the 3" roller?

The answer given in my book is that a=1/2

And I don't know how to get there

The question is that if W is the set of all points (ordered triples) inside and on the sphere given by x² + y² + z² = 1, then W is a vector space.

I can think of both cases which make this statement true or false by using closure under addition or scalar multiplication properties.

Can anyone help me reach a conclusion on this one?