A) \[\sqrt{22}\]
B) 4
C) \[\sqrt{32}\]
D) 6
Correct Answer: D
Solution :
Projection of \[\vec{b}\]on \[\vec{a}\] \[=\frac{\vec{a}.\vec{b}}{\left| {\vec{a}} \right|}=\left| {\vec{a}} \right|\] | ||
\[\Rightarrow \] \[{{b}_{1}}+{{b}_{2}}=-10\] | ? (1) | |
and \[\left( \vec{a}+\vec{b} \right)\bot \vec{c}\] \[\Rightarrow \] \[\left( \vec{a}+\vec{b} \right).\vec{c}=0\] | ||
\[\Rightarrow \] \[5{{b}_{1}}+{{b}_{2}}=-10\] | ? (2) | |
from [a] and (2) | ||
\[\Rightarrow \] \[{{b}_{1}}=-\,3\] and \[{{b}_{2}}=5\] | ||
then, \[\left| {\vec{b}} \right|=\sqrt{b_{1}^{2}+b_{2}^{2}+6.}\] | ||
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