Dot product of two vectors..

[elleocin]

Given a and b unit vectors..

a. if the angle between them is 60 degrees, calculate (6a+b) • (a-2b)

My answer: |6a+b||a-2b|cos60
=(6 + 0 + 0 -2)cos60
=4cos60
=2 <----- the answer is supposed to be -3/2

Help would be appreciated!

 

[Deleted member 4993]

Given a and b unit vectors..

a. if the angle between them is 60 degrees, calculate (6a+b) • (a-2b) → 6 - 12a•b + a•b -2 and a•b = cos(60°).... continue

My answer: |6a+b||a-2b|cos60
=(6 + 0 + 0 -2)cos60
=4cos60
=2 <----- the answer is supposed to be -3/2

Help would be appreciated!

.

 

[elleocin]

Don't unit vectors that are not the same = 0? So wouldn't I still get the same answer with your equation?

 

[pka]

Don't unit vectors that are not the same = 0? So wouldn't I still get the same answer with your equation?

NO!
\(\displaystyle \vec{a}\cdot\vec{a}=1\) and \(\displaystyle \vec{a}\cdot\vec{b}=\cos(60^o)=0.5\)

 

[elleocin]

Oh, I see it now!

But would you mind explaining the background info on how a•b = cos60? Is it just because it is worded in the question?

Thanks

 

[Bob Brown MSEE]

Don't unit vectors that are not the same = 0? So wouldn't I still get the same answer with your equation?

You may be confusing a pair of unit vectors with a pair of orthonormal basis vectors.
Both types of pairs have length 1.

a and b are not orthogonal, they are at 60 degrees.

 

[elleocin]

:idea:

Thank you Bob!