find |2a+b|^2, if |vector b|=5, |vector a|=4 |2a-b|=7

[pay2joy2]

find |2a+b|^2, if |vector b|=5, |vector a|=4 |2a-b|=7 , been stuck for hour.

 

[blamocur]

Can you expand |2a+b|^2 ? How about |2a-b|^2 ?

 

[pka]

find |2a+b|^2, if |vector b|=5, |vector a|=4 |2a-b|=7 , been stuck for hour.

Your notation leaves much to be desired.
Are we to assume that the following is correct?
${\left\| {\overrightarrow a + \overrightarrow b } \right\|^2} = \left( {\overrightarrow a + \overrightarrow b } \right) \cdot \left( {\overrightarrow a + \overrightarrow b } \right)$

 

[pay2joy2]

Your notation leaves much to be desired.
Are we to assume that the following is correct?
${\left\| {\overrightarrow a + \overrightarrow b } \right\|^2} = \left( {\overrightarrow a + \overrightarrow b } \right) \cdot \left( {\overrightarrow a + \overrightarrow b } \right)$

So, the a and b is vector coordinates, and |a| is lenght of vector, same as |2a-b|. I'm sorry that's all i can give you, that's how the task was given to me.

 

[topsquark]

find |2a+b|^2, if |vector b|=5, |vector a|=4 |2a-b|=7 , been stuck for hour.

Hint: $\mid 2 \textbf{a} - \textbf{b} \mid ^2 = (2 \textbf{a} - \textbf{b} ) \cdot (2 \textbf{a} - \textbf{b} ) = 4 a^2 + b^2 - 4 \textbf{a} \cdot \textbf{b}$.

How does this help?

-Dan

 

[pka]

So, the a and b is vector coordinates, and |a| is lenght of vector, same as |2a-b|. I'm sorry that's all i can give you, that's how the task was given to me.
View attachment 34121

If we use ${\left\| {\overrightarrow a } \right\|^2} = \overrightarrow a ~\overrightarrow { \cdot a}$
That tells us that $\overrightarrow a \; \cdot \;\overrightarrow a = 16~\&~\overrightarrow b \; \cdot \;\overrightarrow b = 25$.
Can you explain why?
Now use reply #5 to finish!