A) 9
B) 6
C) 5
D) 4
Correct Answer: B
Solution :
Here |a|=4; \[|\mathbf{b}|=4;\,\,\,|\mathbf{c}|=2\] and \[\mathbf{a}.(\mathbf{b}+\mathbf{c})=0\Rightarrow \mathbf{a}.\mathbf{b}+\mathbf{a}\mathbf{.c}=0\] .....(i) \[\mathbf{b}.(\mathbf{c}+\mathbf{a})=0\Rightarrow \mathbf{b}\mathbf{.c}+\mathbf{b}\mathbf{.a}=0\] .....(ii) \[\mathbf{c}.(\mathbf{a}+\mathbf{b})=0\Rightarrow \mathbf{c}\mathbf{.a}+\mathbf{c}\mathbf{.b}=0\] .....(iii) Adding (i), (ii) and (iii), we get, \[2[\mathbf{a}\mathbf{.b}+\mathbf{b}\mathbf{.c}+\mathbf{c}\mathbf{.a}]=0\] \ \[|\mathbf{a}+\mathbf{b}+\mathbf{c}|=\sqrt{|\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+|\mathbf{c}{{|}^{2}}+2(\mathbf{a}.\mathbf{b}+\mathbf{b}.\mathbf{c}+\mathbf{c}.\mathbf{a})}\] \[=\sqrt{|\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+|\mathbf{c}{{|}^{2}}}\]=\[\sqrt{16+16+4}\] Þ \[|\mathbf{a}+\mathbf{b}+\mathbf{c}|=6\].You need to login to perform this action.
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