Find the value of ( a - 5 b ) · ( 2 a + b ) :

Question

Find the value of $(\vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + \vec{b})$ :

Smart Achievers · Accepted Answer

(1)

Ans. $2 | \vec{a} |^{2} - 9 \vec{a} \cdot \vec{b} - 5 | \vec{b} |^{2}$

Explanation:

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

$= 2 \vec{a} \cdot \vec{a} + \vec{a} \cdot \vec{b} - 10 \vec{a} \cdot \vec{b} - 5 \vec{b} \cdot \vec{b}$

$= 2 | \vec{a} |^{2} - 9 \vec{a} \cdot \vec{b} - 5 | \vec{b} |^{2}$

Solution

Q.
Find the value of $(\vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + \vec{b})$ :

1 $2 | \vec{a} |^{2} - 9 \vec{a} \cdot \vec{b} - 5 | \vec{b} |^{2}$

2 $| \vec{a} |^{2} + 5 \vec{a} \cdot \vec{b} - 9 | \vec{b} |^{2}$

3 $| \vec{a} |^{2} + 5 \vec{a} \cdot \vec{b} + | \vec{b} |^{2}$

4 $| \vec{a} |^{2} + \vec{a} \cdot \vec{b} + | \vec{b} |^{2}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Find the value of (a→-5b→)·(2a→+b→):

1 2|a→|2-9a→·b→-5|b→|2

2 |a→|2+5a→·b→-9|b→|2

3 |a→|2+5a→·b→+|b→|2

4 |a→|2+a→·b→+|b→|2