Given a and b unit vectors, determine (2a-5b) . (b+3a)
if |a+b| =sqrt3
all a and b in the questions have a u-hat over top of them=unit vectors
can someone please check my work:
|a+b|=sqrt3
|a+b|^(0.5)=(a+b)(a+b)
3=2+2a.b
0.5=a.b
(2a-5b). (b+3a)
=-13a.b+6(a)^2-5(b)^2
=-13(0.5)+6(1)^2-5(1)^2
=-5.5
is my answer correct? mostly concerned about the a.b work
that's what I did, BUT, is a.b OK or do I have to do something with cos(theta)=0.5
I dont think I do, because I already found a.b, correct? so just plug it into the eqtn below, right?
|a+b|=sqrt3
|a+b|^(0.5)=(a+b)(a+b)
3=2+2a.b
0.5=a.b
(2a-5b). (b+3a)
=-13a.b+6(a)^2-5(b)^2
=-13(0.5)+6(1)^2-5(1)^2
=-5.5