[SOLVED] vector Problem

**a.a** · May 25th 2008, 12:40 PM

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....

**Moo** · May 25th 2008, 01:07 PM

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 ?

**a.a** · May 25th 2008, 01:13 PM

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

**Moo** · May 25th 2008, 01:16 PM

Originally Posted by a.a

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

I get it too ^^

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