A) \[\mathbf{r}.(-30\mathbf{i}+13\mathbf{j}+5\mathbf{k})=4\]
B) \[\mathbf{r}.(30\mathbf{i}+13\mathbf{j}+5\mathbf{k})=4\]
C) \[\mathbf{r}.(30\mathbf{i}+13\mathbf{j}-5\mathbf{k})=4\]
D) \[\mathbf{r}.(30\mathbf{i}-13\mathbf{j}-5\mathbf{k})=4\]
Correct Answer: A
Solution :
Let the equation of plane is \[a(x+1)+b(y+2)+c(z-0)=0\] ?..(i) As it passes through (2, 3, 5) so, \[3a+5b+5c=0\] ?..(ii) also, \[2a+5b-c=0\] ?..(iii) \[\therefore \]\[\frac{a}{-5-25}=\frac{b}{10+3}=\frac{c}{15-10}\] \[\therefore \] \[\frac{a}{-30}=\frac{b}{13}=\frac{c}{5}\] Hence equation of plane is, \[-30x+13y+5z=4\] or \[\mathbf{r}.(-30\mathbf{i}+13\mathbf{j}+5\mathbf{k})=4\].You need to login to perform this action.
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