A) \[\mathbf{p}-4\mathbf{q}\]
B) \[\frac{-7\mathbf{q}+\mathbf{r}}{5}\]
C) \[2\mathbf{p}-3\mathbf{q}+\mathbf{r}\]
D) \[4\mathbf{p}-2\mathbf{r}\]
Correct Answer: B
Solution :
Let \[-2\mathbf{a}+3\mathbf{b}-\mathbf{c}=x\mathbf{p}+y\mathbf{q}+z\mathbf{r}\] \[\Rightarrow \]\[-2\mathbf{a}+3\mathbf{b}-\mathbf{c}\] \[=(2x+y-3z)\mathbf{a}+(-3x-2y+z)\mathbf{b}+(y+2z)\mathbf{c}\] \[\therefore \,2x+y-3z=-2,\] \[-3x-2y+z=3\] and \[y+2z=-1\] Solving these, we get \[x=0,\] \[y=-\frac{7}{5},\] \[z=\frac{1}{5}\] \ \[-2\mathbf{a}+3\mathbf{b}-\mathbf{c}=\frac{(-7\mathbf{q}+\mathbf{r})}{5}.\] Trick : Check alternates one by one i.e., (a) \[\mathbf{p}-4\mathbf{q}=-2\mathbf{a}+5\mathbf{b}-4\mathbf{c}\] (b) \[\frac{-7\mathbf{q}+\mathbf{r}}{5}=-2\mathbf{a}+3\mathbf{b}-\mathbf{c}\].
You need to login to perform this action.
You will be redirected in
3 sec
