Gr 12. Vector problem!

**narutoblaze** · February 15th 2009, 12:20 PM

Given a and b unit vectors.
a) if the angle between them is 60deg, calculate (6a + b) dot (a - 2b)
b) if |a + b| = root 3, determine (2a - 5b) dot (b + 3a)
a and b are unit vectors

Please and thank you!

**TheEmptySet** · February 15th 2009, 12:59 PM

Originally Posted by narutoblaze

Given a and b unit vectors.
a) if the angle between them is 60deg, calculate (6a + b) dot (a - 2b)
b) if |a + b| = root 3, determine (2a - 5b) dot (b + 3a)
a and b are unit vectors

Please and thank you!

Dont forget that the dot product is a LINEAR.

$(\vec a + \vec b) \cdot \vec c =\vec a \cdot \vec c +\vec b \cdot \vec c$ for all vectors in you space and

for any real number $\alpha,\beta \in \mathbb{R}$
$(\alpha \vec a) \cdot (\beta \vec b)=\alpha \beta (\vec a \cdot \vec b)$

Also the defintion $\vec a \cdot \vec b= ||a||||b||\cos(\theta)$

using these two properties we get

$(2\vec a-5 \vec b) \cdot (\vec b+\vec 3a) =(2\vec a)\cdot (\vec b+\vec 3a)+(-5\vec b)\cdot (\vec b+\vec 3a)=$

$(2\vec a)\cdot (\vec b)+(2\vec a)\cdot (3\vec a)+(-5\vec b)\cdot (\vec b)+(-5\vec b)\cdot (\vec 3a)=$

$2(\vec a \cdot \vec b)+6(\vec a \cdot \vec a)-5(\vec b \cdot \vec b)-15 (\vec b \cdot \vec a)$

Since a and be are both unit vectors we get

$<br /> 2\cos(60)+6\cos(0)-5\cos(0)-15\cos(60)<br /> <br />$
Just simplify from here

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