# Math Help - [SOLVED] vector Problem

1. ## [SOLVED] vector Problem

Given ^a and ^b are unit vectors and magnitude of ^a + ^ b is sqrt. 3 then determine (2^a - 5^b) dot (^b + 3^a)

From previous parts we are given that the angle os 60 degrees.

So far i.ve got:

(2^a - 5^b) dot (^b + 3^a) = 6 times the magnitude of ^a squred - 5 times the magnitude of ^b squared - 13 ^a dot ^ b

Im not sure where to go from here....

2. Hello,

Originally Posted by a.a
Given ^a and ^b are unit vectors and magnitude of ^a + ^ b is sqrt. 3 then determine (2^a - 5^b) dot (^b + 3^a)

From previous parts we are given that the angle os 60 degrees.

So far i.ve got:

(2^a - 5^b) dot (^b + 3^a) = 6 times the magnitude of ^a squred - 5 times the magnitude of ^b squared - 13 ^a dot ^ b

Im not sure where to go from here....
Since the angle is 60° (which is in harmony with the magnitude of $\vec{a}+\vec{b}$, $\cos \theta=\frac 12$.

Therefore, $\vec{a}.\vec{b}=|\vec{a}| |\vec{b}| \cos \theta=\frac 12 |\vec{a}| |\vec{b}|$

Since $\vec{a}$ and $\vec{b}$ are unit vectors, their magnitude is 1 !

Can you conclude ?

3. ## ans

I got -11/2 as the answer....?

4. Originally Posted by a.a
I got -11/2 as the answer....?
I get it too ^^