A) \[l=\frac{(\mathbf{c}\times \mathbf{b})\,.\,(\mathbf{a}\times \mathbf{b})}{{{(\mathbf{a}\times \mathbf{b})}^{2}}},\,\,m=\frac{(\mathbf{c}\times \mathbf{a})\,.\,(\mathbf{b}\times \mathbf{a})}{{{(\mathbf{b}\times \mathbf{a})}^{2}}}\]
B) \[l=\frac{(\mathbf{c}\times \mathbf{b})\,.\,(\mathbf{a}\times \mathbf{b})}{(\mathbf{a}\times \mathbf{b})},\,\,m=\frac{(\mathbf{c}\times \mathbf{a})\,.\,(\mathbf{b}\times \mathbf{a})}{(\mathbf{b}\times \mathbf{a})}\]
C) \[l=\frac{(\mathbf{c}\times \mathbf{b})\,\times \,(\mathbf{a}\times \mathbf{b})}{{{(\mathbf{a}\times \mathbf{b})}^{2}}},\,\,m=\frac{(\mathbf{c}\times \mathbf{a})\,\times \,(\mathbf{b}\times \mathbf{a})}{(\mathbf{b}\times \mathbf{a})}\]
D) None of these
Correct Answer: A
Solution :
Here \[(l\mathbf{a}+m\mathbf{b})\times \mathbf{b}=\mathbf{c}\times \mathbf{b}\Rightarrow l\mathbf{a}\times \mathbf{b}=\mathbf{c}\times \mathbf{b}\] \[\Rightarrow l{{(\mathbf{a}\times \mathbf{b})}^{2}}=(\mathbf{c}\times \mathbf{b})\,.\,(\mathbf{a}\times \mathbf{b})\Rightarrow l=\frac{(\mathbf{c}\times \mathbf{b})\,.\,(\mathbf{a}\times \mathbf{b})}{{{(\mathbf{a}\times \mathbf{b})}^{2}}}\] Similarly, \[m=\frac{(\mathbf{c}\times \mathbf{a})\,.\,(\mathbf{b}\times \mathbf{a})}{{{(\mathbf{b}\times \mathbf{a})}^{2}}}\].
You need to login to perform this action.
You will be redirected in
3 sec
