# [SOLVED] vector Problem

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• May 25th 2008, 12:40 PM
a.a
[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....
• May 25th 2008, 01:07 PM
Moo
Hello,

Quote:

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 ? :)
• May 25th 2008, 01:13 PM
a.a
ans
I got -11/2 as the answer....?
• May 25th 2008, 01:16 PM
Moo
Quote:

Originally Posted by a.a
I got -11/2 as the answer....?

I get it too ^^