Let a¯,b¯,c¯ be there non-zero, non-collinear vectors such that c¯=a¯×(c¯+b¯) and also given that |a¯|=1,|b¯|=2,|c¯|=3 then the value of |2c¯+(b¯×a¯)+((a¯×b¯)×a¯)|=___

c¯=a¯×c¯+a¯×b¯⇒a¯×c¯=0 a¯×c¯=a¯(a¯×c¯)+a¯(a¯×b¯) a¯⇒ c¯−a×b=−c¯+(a.b)a¯−a¯2b¯ ⇒ 2 c¯+b¯×a¯+(a¯×b¯)×a¯=0

Let a¯,b¯,c¯ be there non-zero, non-collinear vectors such that c¯=a¯×(c¯+b¯) and also given that |a¯|=1,|b¯|=2,|c¯|=3 then the value of |2c¯+(b¯×a¯)+((a¯×b¯)×a¯)|=___

c¯=a¯×c¯+a¯×b¯⇒a¯×c¯=0 a¯×c¯=a¯(a¯×c¯)+a¯(a¯×b¯) a¯⇒ c¯−a×b=−c¯+(a.b)a¯−a¯2b¯ ⇒ 2 c¯+b¯×a¯+(a¯×b¯)×a¯=0

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Let $\bar{a}, \bar{b}, \bar{c}$ be there non-zero, non-collinear vectors such that $\bar{c} = \bar{a} \times (\bar{c} + \bar{b})$ and also given that $| \bar{a} | = 1, | \bar{b} | = 2, | \bar{c} | = 3$ then the value of $| 2 \bar{c} + (\bar{b} \times \bar{a}) + ((\bar{a} \times \bar{b}) \times \bar{a}) | =___$

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Detailed Solution

$\bar{c} = \bar{a} \times \bar{c} + \bar{a} \times \bar{b} \Rightarrow \bar{a} \times \bar{c} = 0 \bar{a} \times \bar{c} = \bar{a} (\bar{a} \times \bar{c}) + \bar{a} (\bar{a} \times \bar{b}) \bar{a} \Rightarrow \bar{c} - a \times b = - \bar{c} + (a . b) \bar{a} - {\bar{a}}^{2} \bar{b} \Rightarrow 2 \bar{c} + \bar{b} \times \bar{a} + (\bar{a} \times \bar{b}) \times \bar{a} = 0$