1. ## Vectors 4

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

2. Originally Posted by skeske1234
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
$\displaystyle 3 = \left( {a + b} \right) \cdot \left( {a + b} \right) = a \cdot a + 2a \cdot b + b \cdot b = 2 + 2a \cdot b$

3. 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

4. Yes you're right but it is:

|a+b|^2 = (a+b).(a+b)

5. sorry, that's what i meant
the squared not the sqrt, but other than that i don't need to use any other formula right