A) \[r=\frac{2}{3}(a+a\times b)\]
B) \[r=\frac{2}{3}(\pm a+a\times b)\]
C) \[r=\frac{1}{4}(\pm \,a+a\times b)\]
D) \[r=\frac{2}{3}(\pm \,a+a\times b)\]
Correct Answer: B
Solution :
Here \[r\times a=b\] \[a\times (r\times a)=a\times b\] \[3r-(a\cdot r)a=a\times b\] \[|r\times a|=|b|\] \[|r|\times |a|\sin \theta =|b|\] \[|r{{|}^{2}}\times |a{{|}^{2}}{{\sin }^{2}}\theta =|b{{|}^{2}}\] \[|r{{|}^{2}}3{{\sin }^{2}}\theta =2\] \[|r{{|}^{2}}(1-{{\cos }^{2}}\theta )=2/3\] \[|r{{|}^{2}}-\frac{2}{3}=|r{{|}^{2}}{{\cos }^{2}}\theta \] \[\frac{1}{3}={{\cos }^{2}}\theta \] \[[\because |r|=1]\] \[3r\bar{+}a=a\times b\] \[r=\frac{1}{3}(a\times b\pm a)\]
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