Given that a = (3,4,0) and a.(a+b)=7, what is the value of a.b?

Question

unklerhaukus · Answer

im not sure what you mean by     a=(3,4,0)
is that a vector or a set?

anonymous · Answer

It's a vector

amistre64 · Answer

distribute, is my thought

terenzreignz · Answer

(a+b) could be many things, my preference being a+b = <1,1,0> that means b = <-2,-3,0>

amistre64 · Answer

a.a + a.b = 7

a.b = 7/(a.a)

amistre64 · Answer

- a.a

terenzreignz · Answer

But @amistre64 aren't there infinitely many solutions for a+b? <1,1,0> is one of them, another would be $$\Large <0,\frac74,0>$$ meaning $$\Large b = \left<-3 , -\frac{9}{4},0\right>$$

amistre64 · Answer

doesnt matter what a+b actually is, the questions asks to determine a.b with whats given.

terenzreignz · Answer

oh right... lol I'm sorry, I must have misread it as a+b

awkwaaard

I must be getting drowsy :3

amistre64 · Answer

a.(a+b)

  3  ,   4 ,     0
3+x, 4+y, 0+z
----------------
9+3x+16+4y


a.a

3 4 0
3 4 0
-----
9+16


a.b

3 4 0
x y z
-----
3x+4y 

a.(a+b) = a.a+a.b = 7

a.b = 7 - a.a = 7 - 25

anonymous · Answer

Thank You : )