Math, asked by TheLifeRacer, 9 months ago

important question for 12th board .

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Answered by kaushik05
7

Given:

 \star \:  \vec{a} +  \vec{b} +  \vec{c} = 0

 \star \:  | \vec{a}|  = 3 \\  \\ \star \:   | \vec{b} = 5|  \\  \\  \star \:  | \vec{c}|  = 7

To find :

• Angle between a and b .

Solution :

 \leadsto \:  \vec{a} +  \vec{b} +  \vec{c} = 0 \\  \\  \leadsto \:  \vec{a} +  \vec{b} =  -  \vec{c}

Now , Square both sides we get ,

 \leadsto \:  { | \vec{a}| }^{2}  +  | { \vec{b}}^{2} |  + 2 | \vec{a}|  | \vec{b}|  =   | { \vec{c}}^{2} |

As we know that : a.b = ab cos @

 \leadsto \:  | { \vec{a}}^{2} |  +  | { \vec{b}}^{2} |  + 2 \:  | \vec{a}|   | \vec{b}|  \cos( \alpha )  =  | { \vec{c}}^{2} |  \\  \\  \leadsto \:  3^{2}  +  {5}^{2}  + 2(3)(5)  \cos( \alpha )  =  {7}^{2}  \\  \\  \leadsto \: 34 + 30 \cos( \alpha )  = 49 \\  \\  \leadsto \:  \cos( \alpha )  = \cancel{  \frac{15}{30}}  \\  \\  \leadsto \cos( \alpha )  =  \frac{1}{2}  \\  \\  \leadsto \:  \alpha  = 60 \degree

Hence , the angle between a and b is 60°

Answered by rajdheerajcreddy
4

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